Question

Kate has some $\$50$ and $\$20$ bills that sum up to $\$500$. The ratio of the number of $\$50$ bills to $\$20$ bills is 3 : 5. Find the number of $\$50$ and $\$20$ bills with Kate.

• A. 6, 10
• B. 7, 12
• C. 8,9
• D. 5,12

Answer 1

The correct option is A 6, 10

Ratio of $\$50$ bills to $\$20$ bills = $3:5$.
Let the number of $\$50$ bills be $3x$ and the number of $\$20$ bills be $5x$, respectively.
We get $3x:5x=3:5$.
Contribution of $\$50$ notes $=3x\times 50$
Contribution of $\$20$ notes $=5x\times 20$
According to the question,
Contribution of $\$50$ notes + contribution from $\$20$ notes = $\$500$
$\Rightarrow 3x\times 50+5x\times 20=500$
$\Rightarrow 150x+100x=500$
$\Rightarrow 250x=500$
$\Rightarrow x=\frac{500}{250}=2$
Number of $\$50$ notes $=3x=3\times 2=6$
Number of $\$20$ notes $=5x=5\times 2=10$