Stacy and Josh

Question

Stacy and Josh both have the same amount of coins. They have only dimes and nickels. Josh has the same number of dimes as Stacy has nickels. Josh has $1.05, Stacy has $1.20. He many of each coin do they have?

Answer 1

X + N = D + X where X is the # of nickles Stacy has = # of dimes Josh has;
N is the # of nickles Josh has
D is the # of dimes Stacy has

N = D is the same as the number of dimes Stacy has

10X + 5N = 105

10D + 5X = 120

N = D

Three equations with three unknowns:
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substitutes n for d in the first equation.
10x + 5d = 105

10D + 5x = 120

solves the first equation for d:
5d = 105 - 10x

d = 21 - 2x
Substitutes into the second equation:

10(21-2x) + 5x = 120
210 - 20x + 5x = 120

-15x = -90
x = 6

Stacy has 6 nickles and Josh has 6 dimes.

D = 21 -2(6) = 21 -12 = 9
Stacy has 9 dimes and Josh has 9 nickles.

Stacy: 5x6 + 9 x 10 = 30 + 90 = 120 cents = $1.20
Josh: 6 x 10 + 9 x 5 = 60 + 45 = 105 = $1.05
The answers are highlighted in bold above and are PROVEN to be Correct