Question

Alexandra has $2.10 worth of nickels and dimes. She has a total of 27 nickels and dimes all together. Determine the number of nickels and dimes that Alexandra has by writing and solving a system of equations. I need to use substitution or elimination to solve this.

Answer 1

Answer:the number of nickels is 12

the the number of dimes is 15

Explanation:

Let x represent the the number of nickels.

Let y represent the the number of dimes.

A nickel is worth 5 cents = 5/100 = $0.05

A dime is worth 10 cents = 10/100 = $0.1

Alexandra has $2.10 worth of nickels and dimes. This means that

0.05x + 0.1y = 2.10 - - - - - - - - - -1

She has a total of 27 nickels and dimes all together. This means that

x + y = 27

Substituting x = 27 - y into equation 1, it becomes

0.05(27 - y) + 0.1y = 2.10

1.35 - 0.05y + 0.1y = 2.1

- 0.05y + 0.1y = 2.1 - 1.35

0.05y = 0.75

y = 0.75/0.05 = 15

Substituting y = 15 into x = 27 - y, it becomes

x = 27 - 15 = 12