Let “D” = number of dimes
Let “N” = number of nickels = D+2
.05N + .10D = 3.70……EQ1, the total value of dimes and
nickels is $3.70, given
.05(D+2) + .10D = 3.70……substitute for “N”
5(D+2) + 10D = 370…….multiply every term by 100 to
eliminate decimals
5D + 10 + 10D = 370…….distribute 5 through parenthesis
15D + 10 = 370…….combine like terms
15D = 360…….subtraction 10 from each side
∴ D = 26……division both sides by 15
N = D + 2….given
= 26 + 2…substitute for “D”
∴ N = 28……..simplify, addition property
Let’s check our work by substituting our answers into the original equation
.05(N) + .10(D) = 3.70…original equation EQ1
.05(28) + .10(26) = 3.70…substitute for “N” and “D”
1.30 + 2.40 = 3.70…simplify
3.70 = 3.70…True, √. Our answers are correct.
Always check your work!
Answer:
Aminata has 26 dimes and 28 nickels totaling $3.70.