Question 214173
Joshua had 142 coins, all nickels and quarters.
 The total amount was $15.30. 
HOw many coins of each type did he have?
:
Let n = no. of nickels; let q = no. of quarters
:
write an equation for each statement:
:
"Joshua had 142 coins,"
n + q = 142
:
"The total amount was $15.30."
.05n + .25q = 15.30
:
 HOw many coins of each type did he have?
:
Go back to the 1st equation, and arrange it for substitution in the 2nd equation
n + q = 142
q = (142-n)
:
Replace q with (42-n) in the 2nd equation, find n
.05n + .25(142-n) = 15.30
:
Multiply what's inside the brackets
.05n + 35.5 - .25n = 15.30
;
.05n - .25n = 15.30 - 35.50
:
-.20n = -20.20
n = {{{(-20.20)/(-.2)}}}; minus into a minus is plus
n = +101 nickels
:
Find q:
q = 142 - 101
q = 41 quarters
:
:
See if this is right, substitute for n and q
.05(101) + .25(41) = 15.30
5.05 + 10.25 = 15.30; confirms our solution
:
Make sense to you?