Question

A collection of quarters and nickels is worth $14.80. There are 88 coins in all.

How many of each coin are there?

Answer 1

so the equaiton is

number of nickes=n
number of quarters=q

if you have 1 quarter then you have 25 cents so we will represent like this
25q

and nickles is 5n
14.50=1450 cents

so
25q+5n=1480
q+n=88
subtract q from both sides
n=88-q
subsitute into first equation
25q+5(88-q)=1480
25q+440-5q=1480
add like terms
20q+440=1480
subtract 440 from both sides
20q=1040
divide both sdies by 20
q=52
there were 52 quarters
25(52)+5n=1480
1300+5n=1480
subtract 1300 from both sides
5n=180
divide both sides by 5
n=36
there were 36 nickels


nickles=36
quarters=52