A cash box contains $74 made up of quarters, half-dollars, and one-dollar coins. How many coins of each type does the box contain if the number of
half-dollar coins is one more than three-fifths of the number of one-dollar
coins and the number of quarters is four times the number of one-dollar
and half-dollar coins together?

25 one-dollar coins, 16 half-dollar coins, and 164 quarters

Step-by-step explanation:

First, set up equations based on the information given:

Then, substitute q in the first equation with the expression from the third equation:

Next, substitute h in that equation with the expression from the second equation:

Solve for d, the number of one-dollar coins:

Substitute 25 for d in the second equation to find h, the number of half-dollar coins:

Substitute 25 for d and 16 for h in the third equation to find q, the number of quarters:

Then, verify that the coins total $74:

Next, verify that the number of half-dollar coins is one more than three-fifths of the number of one-dollar coins:

Finally, verify that the number of quarters is four times the number one-dollar and half-dollar coins together:

relating to or denoting a system of numbers and arithmetic based on the number ten, tenth parts, and powers of ten.

step-by-step explanation:

eve and marks ratios are equivalent

step-by-step explanation: