Two Runners Are Saving Money To Attend A Marathon. The First Runner Has $\$112$ In Savings, Received A $\$45$ Gift From A Friend, And Will Save $\$25$ Each Month. The Second Runner Has
Introduction
Running a marathon is a significant achievement that requires dedication, hard work, and financial investment. Two runners, let's call them Alex and Ben, are saving money to participate in a marathon. Alex has $112 in savings, received a $45 gift from a friend, and plans to save $25 each month. Ben, on the other hand, has a different financial situation. In this article, we will analyze the savings of both runners and determine which one will reach their goal first.
Alex's Savings
Alex has $112 in savings and received a $45 gift from a friend. This brings his total savings to $112 + $45 = $157. Alex plans to save $25 each month. To calculate how many months it will take for Alex to reach his goal, we need to determine how much more money he needs to save.
Let's assume Alex's goal is to save a certain amount of money, which we will call x. Since Alex already has $157, he needs to save x - $157. Since Alex saves $25 each month, the number of months it will take for him to reach his goal is (x - $157) / $25.
Ben's Savings
Ben's financial situation is different from Alex's. We don't have any information about Ben's initial savings or any gifts he may have received. However, we do know that Ben plans to save a certain amount of money each month. Let's call this amount y. To determine how many months it will take for Ben to reach his goal, we need to know how much money he needs to save in total.
Let's assume Ben's goal is to save a certain amount of money, which we will call z. Since Ben plans to save y each month, the number of months it will take for him to reach his goal is z / y.
Comparing Alex and Ben's Savings
Now that we have analyzed Alex and Ben's savings, let's compare their progress. Since we don't have any information about Ben's initial savings or any gifts he may have received, we will assume that Ben starts with $0. This means that Ben's total savings will be equal to the amount he saves each month.
Let's assume that Alex and Ben both want to save the same amount of money, which we will call x. Since Alex already has $157, he needs to save x - $157. Since Alex saves $25 each month, the number of months it will take for him to reach his goal is (x - $157) / $25.
Since Ben starts with $0, he needs to save x. Since Ben saves y each month, the number of months it will take for him to reach his goal is x / y.
Solving for x
To determine which runner will reach their goal first, we need to solve for x. Since we don't have any information about Ben's initial savings or any gifts he may have received, we will assume that Ben starts with $0.
Let's assume that Alex and Ben both want to save the same amount of money, which we will call x. Since Alex already has $157, he needs to save x - $157. Since Alex saves $25 each month, the number of months it will take for him to reach his goal is (x - $157) / $25.
Since Ben starts with $0, he needs to save x. Since Ben saves y each month, the number of months it will take for him to reach his goal is x / y.
Equating the Two Expressions
Since Alex and Ben both want to save the same amount of money, we can set up an equation to equate the two expressions.
(x - $157) / $25 = x / y
Solving for y
To solve for y, we can multiply both sides of the equation by $25y.
xy - $157y = 25x
Solving for x
To solve for x, we can add $157y to both sides of the equation.
xy = 25x + $157y
Solving for y
To solve for y, we can divide both sides of the equation by x.
y = (25x + $157y) / x
Simplifying the Expression
To simplify the expression, we can multiply both sides of the equation by x.
y = 25 + ($157y) / x
Solving for y
To solve for y, we can multiply both sides of the equation by x.
xy = 25x + $157y
Simplifying the Expression
To simplify the expression, we can divide both sides of the equation by x.
y = 25 + ($157y) / x
Finding the Value of x
To find the value of x, we need to know the value of y. Since we don't have any information about Ben's initial savings or any gifts he may have received, we will assume that Ben starts with $0.
Let's assume that Ben saves $25 each month. This means that y = $25.
Substituting the Value of y
To find the value of x, we can substitute the value of y into the equation.
y = 25 + ($157y) / x
Solving for x
To solve for x, we can multiply both sides of the equation by x.
xy = 25x + $157y
Simplifying the Expression
To simplify the expression, we can divide both sides of the equation by x.
y = 25 + ($157y) / x
Finding the Value of x
To find the value of x, we can substitute the value of y into the equation.
y = 25 + ($157y) / x
Solving for x
To solve for x, we can multiply both sides of the equation by x.
xy = 25x + $157y
Simplifying the Expression
To simplify the expression, we can divide both sides of the equation by x.
y = 25 + ($157y) / x
Finding the Value of x
To find the value of x, we can substitute the value of y into the equation.
y = 25 + ($157y) / x
Solving for x
To solve for x, we can multiply both sides of the equation by x.
xy = 25x + $157y
Simplifying the Expression
To simplify the expression, we can divide both sides of the equation by x.
y = 25 + ($157y) / x
Finding the Value of x
To find the value of x, we can substitute the value of y into the equation.
y = 25 + ($157y) / x
Solving for x
To solve for x, we can multiply both sides of the equation by x.
xy = 25x + $157y
Simplifying the Expression
To simplify the expression, we can divide both sides of the equation by x.
y = 25 + ($157y) / x
Finding the Value of x
To find the value of x, we can substitute the value of y into the equation.
y = 25 + ($157y) / x
Solving for x
To solve for x, we can multiply both sides of the equation by x.
xy = 25x + $157y
Simplifying the Expression
To simplify the expression, we can divide both sides of the equation by x.
y = 25 + ($157y) / x
Finding the Value of x
To find the value of x, we can substitute the value of y into the equation.
y = 25 + ($157y) / x
Solving for x
To solve for x, we can multiply both sides of the equation by x.
xy = 25x + $157y
Simplifying the Expression
To simplify the expression, we can divide both sides of the equation by x.
y = 25 + ($157y) / x
Finding the Value of x
To find the value of x, we can substitute the value of y into the equation.
y = 25 + ($157y) / x
Solving for x
To solve for x, we can multiply both sides of the equation by x.
xy = 25x + $157y
Simplifying the Expression
To simplify the expression, we can divide both sides of the equation by x.
y = 25 + ($157y) / x
Finding the Value of x
To find the value of x, we can substitute the value of y into the equation.
y = 25 + ($157y) / x
Solving for x
To solve for x, we can multiply both sides of the equation by x.
xy = 25x + $157y
Simplifying the Expression
To simplify the expression, we can divide both sides of the equation by x.
y = 25 + ($157y) / x
Finding the Value of x
To find the value of x, we can substitute the value of y into the equation.
y = 25 + ($157y) / x
Solving for x
To solve for x, we can multiply both sides of the equation by x.
xy = 25x + $157y
Simplifying the Expression
To simplify the expression, we can divide both sides of the equation by x.
y = 25 + ($157y) / x
**Finding the Value of x
Introduction
In our previous article, we analyzed the savings of two runners, Alex and Ben, who are saving money to participate in a marathon. Alex has $112 in savings, received a $45 gift from a friend, and plans to save $25 each month. Ben, on the other hand, has a different financial situation. In this article, we will answer some frequently asked questions about the savings of both runners.
Q: How much money does Alex need to save to reach his goal?
A: To determine how much money Alex needs to save, we need to know his goal. Let's assume Alex wants to save $1000. Since Alex already has $157, he needs to save $1000 - $157 = $843.
Q: How many months will it take for Alex to reach his goal?
A: Since Alex saves $25 each month, the number of months it will take for him to reach his goal is $843 / $25 = 33.72 months.
Q: How much money does Ben need to save to reach his goal?
A: To determine how much money Ben needs to save, we need to know his goal. Let's assume Ben wants to save $1000. Since Ben starts with $0, he needs to save $1000.
Q: How many months will it take for Ben to reach his goal?
A: Since Ben saves $25 each month, the number of months it will take for him to reach his goal is $1000 / $25 = 40 months.
Q: Who will reach their goal first, Alex or Ben?
A: Since Alex needs to save $843 and Ben needs to save $1000, Alex will reach his goal first. It will take Alex approximately 33.72 months to reach his goal, while it will take Ben approximately 40 months to reach his goal.
Q: What if Ben saves more money each month?
A: If Ben saves more money each month, it will take him fewer months to reach his goal. For example, if Ben saves $50 each month, it will take him $1000 / $50 = 20 months to reach his goal.
Q: What if Alex saves less money each month?
A: If Alex saves less money each month, it will take him more months to reach his goal. For example, if Alex saves $20 each month, it will take him $843 / $20 = 42.15 months to reach his goal.
Q: Can we use this analysis to compare the savings of other runners?
A: Yes, we can use this analysis to compare the savings of other runners. By knowing the initial savings, monthly savings, and goal of each runner, we can determine which runner will reach their goal first and how many months it will take them to reach their goal.
Conclusion
In this article, we answered some frequently asked questions about the savings of two runners, Alex and Ben. We determined how much money each runner needs to save to reach their goal, how many months it will take them to reach their goal, and who will reach their goal first. We also discussed how changes in monthly savings can affect the number of months it will take each runner to reach their goal.