Question

Max has a collection of dimes and quarters. He has 25 coins that total $3.70. What is the best method to use to find the number of quarters in the collection?

Answer 1

To find the number of quarters in Max's collection, we can set up a system of equations and solve. Using either the substitution or elimination method, we find that Max has 17 dimes and 8 quarters.

Step-by-step explanation:

To find the number of quarters in Max's collection, we can use a system of equations. Let's assign variables for the number of dimes and quarters. Let d represent the number of dimes and q represent the number of quarters. Since Max has 25 coins total, we can write the equation d + q = 25. We also know that the total value of the coins is $3.70, which in cents is 370 cents. Each dime is worth 10 cents and each quarter is worth 25 cents, so we can write the equation 10d + 25q = 370.

Next, we can solve this system of equations by substitution or elimination to find the values of d and q. Let's use the substitution method.

1. Solve the first equation for d in terms of q: d = 25 - q
2. Substitute this expression for d in the second equation: 10(25 - q) + 25q = 370
3. Simplify and solve for q: 250 - 10q + 25q = 370, combining like terms gives 15q = 120, so q = 8
4. Substitute the value of q back into the first equation to find d: d + 8 = 25, d = 17

Therefore, Max has 17 dimes and 8 quarters in his collection.

Answer 2

he can only have so many quarters before it goes over the maximum amount of $3.70. if theres 25 coins total of only dimes and quarters, you can find the maximum of them both, which will add up to be $3.70 exactly.