Gianna has 27 coins consisting of dimes and quarters. The total value of her coins is 4.80. How many quarters and how many dimes does she have?

Question

Substitution or elimination problem

 

Algebra 2 level 3

Answer 1

Let d be the number of dimes and q be the number of quarters. We come up with an equation for the number of coins:

 

d + q = 27

 

we can come up with a second equation for the value of the coins

 

0.10d + 0.25q = 4.80

 

Now let's use substitution to solve

 

q = 27 - d

 

 

0.10d + 0.25 ( 27 - d)= 4.80

 

 

0.10d + 6.75 - 0.25d = 4.80

 

-0.15d = -1.95

 

d = 13

 

 

Now substitute into the first equation to solve for q

 

13 + q = 27

 

q = 14

 

 

She has 13 dimes and 14 quarters.

 

 

Answer 2

x = number of dimes

y = number of quarters

 

x + y = 27

x = 27 - y

 

.1x + .25y = 4.8

 

Substitute the equation for x into the second equation:

.1 ( 27 - y) + .25y = 4.8

2.7 - .1y + .25y = 4.8

.15y = 2.1

y = 14

 

So the number of quarters (y) = 14

 

Solve for x

x = 27 - y = 27 - 14 = 13

So the number of dimes (x) = 13

 

Double check

 

13 dimes = $1.30

14 quarters = $3.50

$1.30 + $3.50 = $4.80

It checks!