Answer:
Thus, Sue has 24 dimes and 76 quarters.
steps:
Let d be the number of dimes Sue has and let q be the number of quarters As she has 2140 cents total, a dime is worth 10 cents, and a quarter is worth 25 cents, we obtain the following system of equations:
{ d + q = 100
10 d + 25 q = 2140
From the first equation, we have
d = 100 − q
Substituting that into the second equation, we have
10 ( 100 − q ) + 25 q = 2140
⇒ 1000 − 10 q + 25 q = 2140
⇒ 15 q = 1140
⇒ q= 1140 /15 = 76
Knowing that q = 76 we can substitute that value into the first equation to obtain
d + 76 = 100
∴ d = 24