Question

Sarah has 8 coins worth $1.40. Some of the coins are nickels and some are quarters. a. Let q = the number of quarters and n = the number of nickels. Write an equation relating the number of quarters and nickels to the total number of coins. b. Write an equation relating the value of the quarters and the value of the nickels to the total value of the coins. c. How many of each coin does Sarah have?

Answer 1

a.
`q + n = 8`

b.
`0.25q + 0.05n = 1.40`

c. Sarah has 3 nickels and 5 quarters

Sep-by-step explanation:

Given

Coins = 8

Worth = $1.40

Solving (a): Equation relating to number of coins

From the question, we understand that

q = quarters

n = nickels

The required equation is:

`q + n = 8`

Solving (b): Equation relating to worth of coins

`1\ quarter = \$0.25`

`1\ nickel = \$0.05`

So, the equation is

`0.25q + 0.05n = 1.40`

Solving (c): Values of q and n

Make n the subject of formula in (a)

`n = 8 - q`

Substitute 8 - q for n in (b)

`0.25q + 0.05(8 - q) = 1.40`

`0.25q + 0.4 - 0.05q = 1.4`

Collect Like Terms

`0.25q - 0.05q = 1.4 - 0.4`

`0.20q = 1.0`

Make q the subject of formula

`q = (1.0)/(0.20)`

`q = 5`

Substitute 5 for q in
`n = 8 - q`

`n = 8 - 5`

`n = 3`

Hence;

Sarah has 3 nickels and 5 quarters