Question

Luis is saving money to purchase a new video game. He has a total of 30 coins consisting of nickels and dimes. The value of the coins is $2.20. Let n represent the number of nickels and let d represent the number of dimes. Which system of equations can be used to determine the number of nickels and the number of dimes Luis has?

Answer 1

A) N + D = 30
B) .05N + .1D = 2.20

Multiplying equation A by -.05
A) -.05N -.05D = -1.50 then adding it to B
B) .05N + .1D = 2.20
.05D = .70
Dimes = 14

Nickels = 30 -14 = 16

Answer 2

The number of nickels are 16 and the number of dimes are 14.

Explanation:

As given

Let n represent the number of nickels.

let d represent the number of dimes.

As given

Luis is saving money to purchase a new video game.

He has a total of 30 coins consisting of nickels and dimes.

Than the equation becomes

n + d = 30

As the value of the coins is $2.20.

As 1 nickel = 0.05 dollars

1 dimes = 0.1 dollars

Than the equation becomes

0.05n + 0.1d = 2.20

Simplify the above

`(5n)/(100) +(d)/(10) = (220)/(100)`

L.C.M of (10,100) = 100

Than

5n + 10d = 220

Than two equations are

n + d = 30 and 5n + 10d = 220

Multiply n + d = 30 by 5 and subtracted from 5n + 10d = 220 .

5n - 5n + 10d - 5d = 220 - 150

5d = 70

`d = (70)/(5)`

d = 14

Put in the equation n + d = 30

n + 14 = 30

n = 30 - 14

n = 16

Therefore the number of nickels are 16 and the number of dimes are 14.