From the equation that uses the total number of fruits, solve for one variable in terms of the other (for example, express apples in terms of peaches, or vice versa).

Take the expression you found for one variable and substitute it into the equation with the prices. Then solve that new equation to find the number of peaches.

After you find a possible number of peaches, make sure the numbers of apples and peaches add to 7 and that the total cost really is $17.

In Desmos, let $x$ be the number of apples and $y$ be the number of peaches. Type the two equations:

• x + y = 7
• 2x + 3y = 17

Look at the graph and tap/click where the two lines intersect. Desmos will show the intersection as an ordered pair $(x, y)$.

From the intersection point, read the $y$-value. That $y$-value is the number of peaches Mara bought.

Let $a$ be the number of apples and $p$ be the number of peaches that Mara bought.

From the problem:

• She bought 7 pieces of fruit total, so:

• Apples cost $2 each and peaches cost $3 each, and she spent $17 total, so:

Now we have a system of two equations in two variables.

From the first equation $a + p = 7$, solve for $a$ in terms of $p$:

We will substitute this expression for $a$ into the second equation.

Substitute $a = 7 - p$ into the cost equation $2a + 3p = 17$:

Distribute the 2:

Combine like terms $-2p + 3p$:

Now solve this equation for $p$.

From $14 + p = 17$, subtract 14 from both sides:

So Mara bought $3$ peaches.