Answer:
There are:
- 32 nickels ($0.05 each) and
- 37 dimes ($0.10 each)
in this jar.
Step-by-step explanation:
Here's how to solve this problem without using unknowns or systems of equations.
Assume that all 69 coins in this jar are nickels. What would be the value of all coins in this jar?
[tex]69 \times 0.05 = \$ \; 3.45[/tex], which is [tex]5.30 - 3.45 = \$ \; 1.85[/tex] short of the actual value in the jar. That's well expected. There are dimes in the jar.
Now, for each dime that in the jar, the value is assumed to [tex]0.10 - 0.05 = \$ \; 0.05[/tex] lower than the real value. The value in the jar is underestimated by [tex]\$ \; 1.85[/tex] for all dimes combined. That means that the value in the jar was underestimated for
[tex]\dfrac{\$\;1.85}{\$\;0.10 - \$\;0.05} = 37 \; \text{times}[/tex].
Each dime is underestimated for only once. In other words, there are 37 dimes in this jar.
The rest of the 69 coins are nickels. There are 69 - 37 = 32 nickels in the jar.
Double check the answer:
[tex]\underbrace{32 \times \$\; 0.05}_{\text{nickels}} + \underbrace{37 \times \$ \; 0.10}_{\text{dimes}} = \$ \;5.30[/tex]
