The currency called the dollar can be, split into smaller currencies called dimes, quarters, nickels, and pennies.
We have 34 quarters and 16 dimes in the jar.
Let's represent
Number of dimes = d
Number of quarters = q
Note that:
1 dime = $0.10
1 quarter = $0.25
Our system of equations is given as:
d + q = 50.........Equation 1
d = 50 - q
0.1d + 0.25q = 10.10............Equation 2
We substitute 50 - q for d in Equation 2
0.1(50 - q) + 0.25q = 10.10
5 - 0.1q + 0.25q = 10.10
Collect like terms
- 0.1q + 0.25q = 10.10 - 5
0.15q = 5.1
Divide both sides by 0.15
0.15q/0.15 = 5.1/0.15
q = 34
We have 34 quarters
Solving for the number of dimes. remember:
d = 50 - q
d = 50 - 34
d = 16
We have 16 dimes
Therefore, we have 34 quarters and 16 dimes in the jar.
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