At a currency exchange booth, 4 US dollars (USD) can be exchanged for 5 local credits, and… — SAT

At a currency exchange booth, $4$ US dollars (USD) can be exchanged for $5$ local credits, and $6$ local credits can be exchanged for $15$ reward coupons. Based on these rates, what is the total number of reward coupons that can be obtained in exchange for $24$ USD?

Answer: 75 coupons

Answer

To find the number of reward coupons obtained from

24

USD, we perform a two-step rate conversion. First, convert USD to local credits:

24\text{ USD} \times \frac{5\text{ local credits}}{4\text{ USD}} = 30\text{ local credits}

. Second, convert local credits to reward coupons:

30\text{ local credits} \times \frac{15\text{ coupons}}{6\text{ local credits}} = 75\text{ coupons}

. Thus, the final value is

75

Step-by-Step Solution

Set up a proportion to find the number of local credits equivalent to

24

USD.

30

local credits

Using the exchange rate of

4

USD to

5

local credits, multiply the starting value of

24

USD by the conversion factor

\frac{5}{4}

Set up a proportion to find the number of coupons equivalent to

30

local credits.

75

coupons

Using the exchange rate of

6

local credits to

15

coupons, multiply the

30

local credits by the conversion factor

\frac{15}{6}

Key Concept

Multi-step rate conversion and unit analysis

Question

Answer

Step-by-Step Solution

Key Concept

Common Mistakes

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