Rebecca has $4.15 in quarters and nickels. The number of quarters she has is one less than twice the number of nickels. How many quarters and how many nickels does she have?

Question

Give 2 equations and the nickels and quarters

Answer 1

Hello, Fdsfds,

Let Q and N represent the number of Quarters and Nickels.

We know that Q=2N-1

We also know that 0.25N is the total value of the quarters, and 0.05N is the total value of the nickels.

The value of all the coins is $4.15 and is = to 0.25Q+0.05

$4.15=0.25Q+0.05N

Use the first equation for quarters and put it in this equation, replacing Q:

4.15=(2N-1)+0.05N

Rearrange to find N: N: N=8

Q is 2N-1, or 15 quarters.

Check to see if 8 nickels and 15 quarters add to $4.15.

N = $0.40

Q = $3.75

T = $4.15

I hope this helps,

Bob

Answer 2

Let x = number of quarters and y = number of nickels.

First, multiply by 100 to avoid decimal points.

25x + 5y = 415

x = 2y-1 from description

Substitute for x

25(2y-1) + 5y = 415

50y-25 +5y = 415

55y -25 =415

55y = 440

y = 440/55 = 8

x = 2(8)-1 = 15

Rebeca has 15 quarters and 8 nickels.

Check 15(.25) + 8(.05) = 3.75 + 0.40 = $4.15

Answer 3

Let q = number of quarters

Let n = number of nickels

A quarter is 25 cents and a nickel is 5 cents.

(25)•(number of quarters) + (5)•(number of nickels) = 415

or

25q + 5n = 415

We know that q = twice the number of nickels minus 1 so

q = 2n-1

Substitute q into the first equation then solve for n

25(2n - 1) + 5n = 415

50n - 25 + 5n = 415

55n = 440

n = 440/55 = 8

So number of nickels = 8

Number of quarters = (2)(8) - 1 = 16 - 1 = 15

Number of quarters = 15