## Full Length 2 QR Q13

NS_Tutor_Sophia
Posts: 48
Joined: Tue Aug 01, 2017 11:49 am

### Full Length 2 QR Q13

A student recently asked us why the wages are multiplied by 1.2 or 1.5 to solve the following question: "Elizabeth earns an hourly wage that is 1.25 times Yavuz’s hourly wage. During their annual review, Elizabeth earns a 20% raise while Yavuz earns a 50% raise. What is the ratio of Elizabeth’s new hourly wage to Yavuz’s new hourly wage?"

Suppose an item is worth \$100. If it value stays the same, its new value is 100% of the original value (\$100). If that item increases in value by 20%, its new value is 120% of its original value (\$120). If it decreases in worth by 60%, then its new value is 40% (100% - 60%) of its original value (\$40).

Therefore, if the item increases in value by 20%, we must multiply not by 20% but by 120%, which is equal to multiplying by 1.2: \$100 x 1.2 = \$120. For this reason, we can multiply Elizabeth's wage by 1.2 when she earns a 20% raise, and we can multiply Yavuz's wage by 1.5 when he earns a 50% raise.
Sophia Stone
PCAT Content Manager
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