Question

Erin has quarters and nickels for a total of 16 coins. The value of his coins is $2.60. Let represent the number of quarters and y represent the number of nickels​

Answer 1

Note: Consider we need to find each type of coins he has.

Given:

Erin has quarters and nickels for a total of 16 coins.

The value of his coins is $2.60.

To find:

The number of each type of coins.

Solution:

Let x represent the number of quarters and y represent the number of nickels.

According to the question,

Total coins : $x+y=16$        ...(i)​

Total value : $0.25x+0.05y=2.60$        ...(ii)​

Multiply equation (i) by 0.25 and subtract the result from (ii).

$0.25x+0.05y-0.25(x+y)=2.60-0.25(16)$

$0.25x+0.05y-0.25x-0.25y=2.60-4$

$-0.20y=-1.40$

Divide both sides by -0.20.

$y=7$

Put y=7 in (i).

$x+7=16$

$x=16-7$

$x=9$

Therefore, the number of quarters is 9 and number of nickels is 7.