Final answer:
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.