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Allison went to the grocery store and bought bottles of soda and bottles of juice. Each bottle of soda has 45 grams of sugar and each bottle of juice has 20 grams of sugar. Allison purchased a total of 11 bottles of juice and soda which collectively contain 445 grams of sugar. Write a system of equations that could be used to determine the number of bottles of soda purchased and the number of bottles of juice purchased. Define the variables that you use to write the system.

Sagot :

Using a system of equations, it is found that Allison bought 2 bottles of juice and 9 bottles of soda.

What is a system of equations?

A system of equations is when two or more variables are related, and equations are built to find the values of each variable.

For this problem, the variables are:

  • Variable x: bottles of juice purchased.
  • Variable y: bottles of soda purchased.

Allison purchased a total of 11 bottles of juice, hence:

x + y = 11 -> x = 11 - y.

These 11 bottles contain 445 grams of sugar, hence, considering the amounts of each bottle, we have that:

20x + 45y = 445

Since x = 11 - y:

20(11 - y) + 45y = 445

25y = 225

y = 225/25

y = 9.

x = 11 - y = 11 - 9 = 2.

She bought 2 bottles of juice and 9 bottles of soda.

More can be learned about a system of equations at https://brainly.com/question/24342899

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