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Math

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PROBLEM

Yolanda bought 3×(14+78+112)3 \times\left(\frac{1}{4}+\frac{7}{8}+1 \frac{1}{2}\right) lbs and Sam bought 2×(14+78+112)2 \times\left(\frac{1}{4}+\frac{7}{8}+1 \frac{1}{2}\right) lbs. Who bought more? Explain.

STEP 1

Assumptions1. Yolanda bought 3×(14+78+11)3 \times\left(\frac{1}{4}+\frac{7}{8}+1 \frac{1}{}\right) pounds of cheese.
. Sam bought ×(14+78+11) \times\left(\frac{1}{4}+\frac{7}{8}+1 \frac{1}{}\right) pounds of cheese.
3. We need to determine who bought more cheese without doing any calculations.

STEP 2

We can see that the quantities of cheese that Yolanda and Sam bought are multiples of the same quantity (14+78+112)\left(\frac{1}{4}+\frac{7}{8}+1 \frac{1}{2}\right).

STEP 3

Yolanda bought3 times the quantity (1+78+112)\left(\frac{1}{}+\frac{7}{8}+1 \frac{1}{2}\right), while Sam bought2 times the same quantity.

SOLUTION

Since3 is greater than2, we can conclude that Yolanda bought more cheese than Sam without doing any calculations.
Yolanda bought more cheese than Sam.

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