Question

Alexa has $0.90 worth of nickels and dimes. She has a total of 13 nickels and dimes altogether. By following the steps below, determine the number of nickels, x, and the number of dimes, y, that Alexa has.

Answer 1

Alexa has 8 nickels and 5 dimes.

Explanation:

Let x be the number of nickels and y be the number of dimes that Alexa has.

Write a system of equations to represent the given information:

x + y = 13 (equation 1)

0.05x + 0.10y = 0.90 (equation 2)

Solve equation 1 for x:

x = 13 - y

Substitute x = 13 - y into equation 2:

0.05(13 - y) + 0.10y = 0.90

Simplify and solve for y:

0.65 - 0.05y + 0.10y = 0.90

0.05y = 0.25

y = 5

Substitute y = 5 into equation 1 to find x:

x + 5 = 13

x = 8

Therefore, Alexa has 8 nickels and 5 dimes.

Answer 2

8 nickels, 5 dimes

Explanation:

We set up and solve this system of equations:

5x + 10y = 90------->x + 2y = 18

x + y = 13------------>x + y = 13

-------------

y = 5, x = 8

5 dimes, 8 nickels

`.10(5) + .05(8)`

`.50 + .40 = .90`

`5 + 8 = 13`