<PRE><B>Question 1128491</B>
&lt;br&gt;
Algebraically....&lt;br&gt;
let n = number of nickels
then (87-n) = number of pennies&lt;br&gt;
The total value of the coins (5 cents for each nickel and 1 cent for each penny) was $1.75 = 175 cents.  Write and solve the equation that says that:&lt;br&gt;
{{{5(n)+1(87-n) = 175}}}&lt;br&gt;
You can finish the formal solution.&lt;br&gt;
Informally, using logical reasoning....&lt;br&gt;
(1) If all 87 coins were pennies, that would be only 87 cents; the actual total of 175 cents is 175-87 = 88 cents more than that.
(2) Exchanging a penny for a nickel keeps the same total of 87 coins but increases the total value by 4 cents.
(3) To make up those other 88 cents, the number of nickels needed is 88/4 = 22.&lt;br&gt;
ANSWER: She used 22 nickels and 87-22 = 65 dimes.&lt;br&gt;
CHECK: 22(5)+65(1) = 110+65 = 175</PRE>