sue has 100 dimes and quarters. if the total value of the coins is $21.40, how many of each kind of coin does she have?

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

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