Problem Solving

M7MBA wrote: ↑

Sun Jan 24, 2021 12:15 am

A purse contains 5-cent coins and 10-cent coins worth a total of $1.75. If the 5-cent coins were replaced with 10-cent coins and the 10-cent coins were replaced with 5-cent coins, the coins would be worth a total of $2.15. How many coins are in the purse?

A. 26
B. 27
C. 28
D. 29
E. 30

Answer: A

Solution:

We can create two equations in which a = the initial number of 5-cent coins and b = the initial number of 10-cent coins. We can create the “money” equation by recalling that a 5-cent coin is $0.05 and a 10-cent coin is $0.10; thus:

0.05a + 0.1b = 1.75

And, after we reverse the coinage, we have:

0.1a + 0.05b = 2.15

Let’s add the two equations together:

0.15a + 0.15b = 3.90

0.15(a + b) = 3.9

Dividing each side by 0.15, we find a + b = 3.9/0.15 = 26. Thus, there are 26 coins in the purse.


Answer: A