maggiemo said:

Joe has 26 coins consisting of quarters and dollar coins. The total value is $17

The problem states that q=quarters. I'm supposed to write an equation ____________________________=17

to find out how many quarters.

I tried making a table, but I am confused about value vs number of coins and making a problem to solve it.

You have:

Let \(\displaystyle q =\) the number of quarters

Then \(\displaystyle 26 - q =\) the number of dollar coins

A value of a quarter is worth \(\displaystyle 0.25\) times the value of a dollar coin.

In this equation, we are leaving out the units of money in order not to clutter the equation as much.

You multiply the value of a coin by the number of each coin, respectively. Then you add those products

and set the sum equal to \(\displaystyle 17 \ (dollars).\)

The following equation includes representatiions of the total value of the quarters added

to the total value of the dollar coins to equal 17 dollars in total value.

\(\displaystyle 0.25q + 1(26 - q) = 17\)

Solve this equation for \(\displaystyle q\) to find out the number of quarters.