Question 705956


We will solve this problem using system of LINEAR EQUATIONS:

{{{x + y = 94}}}......eq.1...where {{{x}}} is number of dimes and {{{y}}}is number of quarters

{{{.10x + .25y =19.30}}}....eq.2
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First, we solve eq.1 for {{{x}}}:

{{{x + y = 94}}}......eq.1

{{{x = 94-y}}}........eq.1a

Then, we substitute the solution for {{{x}}}in eq.2:

{{{.10x + .25y =19.30}}}....eq.2

{{{.10(94-y) + .25y =19.30}}}.......solve for {{{y}}}

{{{9.4-.10y + .25y =19.30}}}

{{{.25y-.10y =19.30-9.4}}}

{{{ .15y =9.9}}}

{{{ y =9.9/0.15}}}

{{{ highlight(y =66)}}}......the number of quarters

Now that we know how much quarters there are, we can complete the equation eq.1a and solve it for {{{x}}}:

{{{x = 94-y}}}........eq.1a

{{{x = 94-66}}}

{{{highlight(x = 28)}}}......the number of dimes