Question 81160
This is a problem with 2 equations and 2 unknowns. Any time you have at least as many equations as you have unknowns, you can solve the problem!
Let N= number of Nickels
Let D= number of Dimes
From the given information, you know:
Equation #1: {{{0.05N+0.1D=3.5}}}
The 0.05 is the value (in dollars) of 1 Nickel, and 0.1 is the value (in dollars) of 1 Dime.
Since you know Jill has 50 coins, you can form the second equation from this information:
Equation #2: {{{N+D=50}}}
Now you have your 2 equations and 2 unknowns, so you are good to go!
First, solve Equation #2 for D:
{{{D=50-N}}}
Now that uou have this expression for D, substitute it into Equation #1 and solve for N:
{{{0.05N+0.1(50-N)=3.5}}}
{{{0.05N+5-0.1N=3.5}}}
{{{0.05N-0.1N=-1.5}}}
{{{-0.05N=-1.5}}}
{{{highlight(N=30)}}}
Now that you have a value for N, substitute that in to Equation #2 and solve for D:
{{{N+D=50}}}
{{{30+D=50}}}
{{{highlight(D=20)}}}
Good Luck,
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