Sally has a total of 40 quarters and dimes worth $6.55. How many of each does she have?

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Answer 1 · 2016-12-04T15:41:19

Sally has 23 dimes worth $2.30 and 17 quarters worth $4.25

Let's call the number of dimes Sally has $d$ $d$ and the number of quarters Sally has $q$ $q$ .

We can then write these two equations from the information given in the problem:

$d + q = 40$ $d + q = 40$

$0.1 d + .025 q = 6.55$ $0.1d + .025q = 6.55$

Step 1) Solve the first equation for $d$ $d$ :

$d + q - q = 40 - q$ $d + q - q = 40 - q$

$d + 0 = 40 - q$ $d + 0 = 40 - q$

$d = 40 - q$ $d = 40 - q$

Step 2) Substitute $40 - q$ $40 - q$ for $d$ $d$ in the second equation and solve for $q$ $q$ :

$0.1 (40 - q) + 0.25 q = 6.55$ $0.1(40 - q) + 0.25q = 6.55$

$4 - 0.1 q + 0.25 q = 6.55$ $4 - 0.1q + 0.25q = 6.55$

$4 + 0.15 q = 6.55$ $4 + 0.15q = 6.55$

$4 - 4 + 0.15 q = 6.55 - 4$ $4 - 4 + 0.15q = 6.55 - 4$

$0 + 0.15 q = 2.55$ $0 + 0.15q = 2.55$

$0.15 q = 2.55$ $0.15q = 2.55$

$\frac{0.15 q}{0.15} = \frac{2.55}{0.15}$ $(0.15q)/0.15 = 2.55/0.15$

$q = 17$ $q = 17$

Step 3) Substitute $17$ $17$ for $q$ $q$ into the solution to the first equation in Step 1) and calculate $d$ $d$ ;

$d = 40 - 17$ $d = 40 - 17$

$d = 23$ $d = 23$