Question 1162226
<br>
Solving the problem using two variables is a good exercise in algebraic techniques.<br>
But a solution using a single variable is faster and more efficient.<br>
Let x = # of nickels
Then x+7 = # of dimes<br>
The total value of the coins is $1.60, or 160 cents:<br>
{{{5(x)+10(x+7) = 160}}}
{{{5x+10x+70 = 160}}}
{{{15x = 90}}}
{{{x = 6}}}<br>
ANSWER: She has x=6 nickels and x+7 = 13 dimes<br>
Note solving the problem informally with logical reasoning is also good mental exercise:<br>
(1) set aside the "extra" 7 dimes, with a total value of 70 cents.
(2) that leaves equal numbers of dimes and nickels, with a total value of 90 cents.
(3) Since the value of one dime and one nickel is 15 cents, the number of each coin she still has is 90/15 = 6.
(4)Now bring back the 7 dimes you counted initially, to find that she has 6 nickels and 6+7=13 dimes.<br>