Question

We have a jar of coins, all quarters and dimes. All together, we have 238 coins, and the total value of all coins in the jar is $ 34.6. How many quarters are there in the jar?

Answer 1

To find the number of quarters in the jar, we can set up a system of equations and solve for the unknown variables. Using the method of substitution, we can find that there are 72 quarters in the jar.

Step-by-step explanation:

To solve this problem, we can set up a system of equations. Let's call the number of quarters Q and the number of dimes D. We have two pieces of information: Q + D = 238 (equation 1) and 0.25Q + 0.10D = 34.6 (equation 2).

To solve this system, we can use the method of substitution or elimination. Let's use substitution. From equation 1, we can express Q in terms of D: Q = 238 - D. Substituting this into equation 2, we get 0.25(238 - D) + 0.10D = 34.6.

Simplifying the equation, we have 59.5 - 0.25D + 0.10D = 34.6. Combining like terms, we get -0.15D = -24.9. Dividing both sides by -0.15, we find that D = 166.

Substituting this value back into equation 1, we find that Q = 238 - 166 = 72. Therefore, there are 72 quarters in the jar.