Increase 99 In The Ratio 12 : 11 12:11 12 : 11 .2. The Price Of An Item In The United States Of America Was US$230 On A Particular Day. The Exchange Rate On This Day Was US$1: R17.80. Calculate The Cost Of This Item In Rand Value.3. Determine

1. Increase 99 in the ratio $12:11$

Understanding the Problem

To increase 99 by a certain ratio, we need to understand the concept of ratios and proportions. A ratio is a comparison of two or more numbers, often expressed as a fraction. In this case, we are given a ratio of $12:11$ and we need to find the increase in 99.

Calculating the Increase

To calculate the increase, we need to find the factor by which 99 needs to be multiplied to get the desired result. We can do this by setting up a proportion:

$$\frac{12}{11} = \frac{x}{99}$$

where $x$ is the increase in 99.

Solving for x

To solve for $x$, we can cross-multiply:

$$12 \times 99 = 11 \times x$$

$$1188 = 11x$$

$$x = \frac{1188}{11}$$

$$x = 108$$

Therefore, the increase in 99 is 108.

Conclusion

In this problem, we used the concept of ratios and proportions to calculate the increase in 99 by a certain ratio. We set up a proportion and solved for the unknown variable $x$ to find the increase.

2. The price of an item in the United States of America was US$230 on a particular day. The exchange rate on this day was US$1: R17.80. Calculate the cost of this item in Rand value.

Understanding the Problem

To calculate the cost of an item in Rand value, we need to understand the concept of exchange rates. An exchange rate is the price of one currency in terms of another currency. In this case, we are given an exchange rate of US$1: R17.80 and we need to find the cost of an item that costs US$230.

Calculating the Cost in Rand

To calculate the cost in Rand, we can use the exchange rate to convert the US dollar value to Rand:

$$\text{Cost in Rand} = \text{Cost in US dollars} \times \text{Exchange rate}$$

$$\text{Cost in Rand} = 230 \times 17.80$$

$$\text{Cost in Rand} = 4094$$

Therefore, the cost of the item in Rand value is R4094.

Conclusion

In this problem, we used the concept of exchange rates to calculate the cost of an item in Rand value. We used the exchange rate to convert the US dollar value to Rand and found the cost to be R4094.

3. Determine the value of x in the equation $x^2 + 5x - 6 = 0$

Understanding the Problem

To determine the value of $x$ in the equation $x^2 + 5x - 6 = 0$, we need to understand the concept of quadratic equations. A quadratic equation is a polynomial equation of degree two, which means the highest power of the variable is two. In this case, we are given a quadratic equation and we need to find the value of $x$.

Solving the Quadratic Equation

To solve the quadratic equation, we can use the quadratic formula:

$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$

where $a$, $b$, and $c$ are the coefficients of the quadratic equation.

Plugging in the Values

In this case, we have:

$$a = 1$$

$$b = 5$$

$$c = -6$$

Plugging these values into the quadratic formula, we get:

$$x = \frac{-5 \pm \sqrt{5^2 - 4(1)(-6)}}{2(1)}$$

$$x = \frac{-5 \pm \sqrt{25 + 24}}{2}$$

$$x = \frac{-5 \pm \sqrt{49}}{2}$$

$$x = \frac{-5 \pm 7}{2}$$

Therefore, we have two possible values for $x$:

$$x = \frac{-5 + 7}{2} = 1$$

$$x = \frac{-5 - 7}{2} = -6$$

Conclusion

In this problem, we used the concept of quadratic equations to determine the value of $x$ in the equation $x^2 + 5x - 6 = 0$. We used the quadratic formula to solve the equation and found two possible values for $x$: 1 and -6.

Conclusion

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Q&A: Mathematical Calculations and Exchange Rates

Q: What is the difference between a ratio and a proportion?

A: A ratio is a comparison of two or more numbers, often expressed as a fraction. A proportion is a statement that two ratios are equal. For example, the ratio of 12 to 11 is equal to the ratio of x to 99.

Q: How do I calculate the increase in a number by a certain ratio?

A: To calculate the increase, you need to find the factor by which the number needs to be multiplied to get the desired result. You can do this by setting up a proportion and solving for the unknown variable.

Q: What is an exchange rate, and how do I calculate it?

A: An exchange rate is the price of one currency in terms of another currency. To calculate the exchange rate, you need to know the value of one currency in terms of another currency. For example, if the exchange rate is US$1: R17.80, then the value of one US dollar is equal to 17.80 Rand.

Q: How do I calculate the cost of an item in Rand value?

A: To calculate the cost of an item in Rand value, you need to know the value of the item in US dollars and the exchange rate. You can use the exchange rate to convert the US dollar value to Rand.

Q: What is a quadratic equation, and how do I solve it?

A: A quadratic equation is a polynomial equation of degree two, which means the highest power of the variable is two. To solve a quadratic equation, you can use the quadratic formula, which is:

x = (-b ± √(b^2 - 4ac)) / 2a

Q: How do I determine the value of x in a quadratic equation?

A: To determine the value of x, you need to plug in the values of a, b, and c into the quadratic formula and solve for x.

Q: What are some common mistakes to avoid when working with mathematical calculations and exchange rates?

A: Some common mistakes to avoid include:

• Not understanding the concept of ratios and proportions
• Not using the correct formula to calculate the exchange rate
• Not plugging in the correct values into the quadratic formula
• Not checking the units of measurement

Q: How can I apply mathematical calculations and exchange rates in real-world scenarios?

A: Mathematical calculations and exchange rates are used in a variety of real-world scenarios, including:

• Finance: to calculate interest rates, exchange rates, and investment returns
• Business: to calculate profit margins, costs, and revenue
• Science: to calculate physical quantities, such as distance, speed, and time
• Engineering: to calculate stresses, strains, and loads on structures

Conclusion

In this article, we have discussed mathematical calculations and exchange rates, including ratios and proportions, exchange rates, quadratic equations, and real-world applications. We have also provided answers to common questions and mistakes to avoid when working with mathematical calculations and exchange rates.