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MODELING REAL LIFE You collect $234 selling small and large smoothies. You sell a total of 46 smoothies. How many of each size did you sell?

A photograph of a small smoothie with a label reading 4 dollars and large smoothies with a label reading 6 dollars and 50 cents.

1 Answer

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By creating a system of equations and using substitution, we determined that 26 small smoothies and 20 large smoothies were sold to achieve a total of 46 smoothies and $234 in sales.

We are given a scenario where a total of $234 is collected from selling small and large smoothies. The problem states that the total number of smoothies sold is 46.

The price of a small smoothie is $4 and that of a large smoothie is $6.50. We can formulate a system of equations to solve for the number of small (s) and large (l) smoothies sold. Here are the equations based on the given information:

s + l = 46 (The total number of smoothies sold is 46.)

4s + 6.50l = 234 (The total sales from the smoothies amount to $234.)

To find the number of each size sold, we can use the method of substitution or elimination. Let's use substitution:

Solve the the first equation for s: s = 46 - l

Substitute this expression for s in the second equation: 4(46 - l) + 6.50l = 234

Simplify and solve for l: 184 - 4l + 6.50l = 234 ⇒ 2.50l = 50 ⇒ l = 20

Now, substitute l = 20 into the first equation to find s: s + 20 = 46 ⇒ s = 26

Therefore, 26 small smoothies and 20 large smoothies were sold.

User Steven Graham
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