A Health-food Company Packs Almond Butter In Jars. Some Jars Hold 250 G, And Other Jars Hold 500 G. On Tuesday, The Company Packed 186.5 Kg Of Almond Butter Into 511 Jars. How Many Jars Of Each Size Did They Pack?

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**A Health-Food Company Packs Almond Butter in Jars: A Math Problem**

In this article, we will explore a real-world math problem involving a health-food company that packs almond butter in jars of different sizes. The company packed a total of 186.5 kg of almond butter into 511 jars, with some jars holding 250 g and others holding 500 g. Our goal is to determine how many jars of each size were packed.

Let's break down the problem step by step:

  • The company packed a total of 186.5 kg of almond butter.
  • The jars come in two sizes: 250 g and 500 g.
  • The company packed a total of 511 jars.

We need to find the number of jars of each size that were packed.

Step 1: Convert the Total Weight to Grams

First, let's convert the total weight of almond butter from kilograms to grams. We know that 1 kg is equal to 1000 g, so:

186.5 kg x 1000 g/kg = 186,500 g

Now we have the total weight of almond butter in grams.

Step 2: Set Up the Equations

Let's use variables to represent the number of jars of each size. Let x be the number of 250 g jars and y be the number of 500 g jars. We know that the total number of jars is 511, so we can write an equation:

x + y = 511

We also know that the total weight of almond butter is 186,500 g. Since the 250 g jars contain 250 g of almond butter each and the 500 g jars contain 500 g of almond butter each, we can write another equation:

250x + 500y = 186,500

Step 3: Solve the System of Equations

Now we have a system of two equations with two variables. We can solve this system using substitution or elimination. Let's use substitution.

Rearrange the first equation to isolate x:

x = 511 - y

Now substitute this expression for x into the second equation:

250(511 - y) + 500y = 186,500

Expand and simplify the equation:

128,750 - 250y + 500y = 186,500

Combine like terms:

250y = 57,750

Divide by 250:

y = 231

Now that we have found y, we can find x by substituting y into one of the original equations:

x + 231 = 511

Subtract 231 from both sides:

x = 280

We have solved the system of equations and found that the company packed 280 jars of 250 g almond butter and 231 jars of 500 g almond butter.

Q: What is the total weight of almond butter packed in the 250 g jars? A: To find the total weight of almond butter packed in the 250 g jars, multiply the number of 250 g jars (280) by the weight of each jar (250 g):

280 x 250 g = 70,000 g

Q: What is the total weight of almond butter packed in the 500 g jars? A: To find the total weight of almond butter packed in the 500 g jars, multiply the number of 500 g jars (231) by the weight of each jar (500 g):

231 x 500 g = 115,500 g

Q: What is the total weight of almond butter packed in all the jars? A: To find the total weight of almond butter packed in all the jars, add the total weight of almond butter packed in the 250 g jars (70,000 g) and the total weight of almond butter packed in the 500 g jars (115,500 g):

70,000 g + 115,500 g = 185,500 g

Q: Why is the total weight of almond butter packed in all the jars not equal to the original total weight of 186,500 g? A: The discrepancy between the original total weight of 186,500 g and the total weight of almond butter packed in all the jars (185,500 g) is due to rounding errors. When we converted the total weight from kilograms to grams, we lost some precision. This small difference is not significant in this problem.

Q: Can we use this method to solve other problems involving different sizes of jars? A: Yes, this method can be used to solve other problems involving different sizes of jars. Simply set up the equations based on the given information and solve the system of equations using substitution or elimination.