Question

Max has 40 fruits consisting of Apples, Mangos, and Peaches. Max has 5 more Apples than Mangos. He also has four times as many Apples as Peaches. How many Apples does Max have? Enter your answer by clicking the bubbles.

Answer 1

We know that

• Max has 40 fruits consisting of Apples, Mangos, and Peaches.

,

• Max has 5 more Apples than Mangos.

,

• He also has four times as many Apples as Peaches.

First, we have to express each statement as an algebraic expression.

$x+y+z=40$

Where x is apples, y is mangos, and z is peaches.

Now, there are 5 more apples than mangos.

$x=y+5$

Also, there are four times as many apples as peaches.

$x=4z$

First, we isolate z from the third equation

$z=\frac{4}{x}$

Then, we replace this in the first equation.

$\begin{gathered} x+y+\frac{4}{x}=40 \\ \frac{x^2+4}{x}+y=40 \end{gathered}$

As you can observe this new equation can be solved with the second equation because both have x and y only.

$\left\{ \begin{aligned}\frac{x^2+4}{x}+y=40 \\ x-y=5\end{aligned}\right.$

We eliminate y, and sum the equations

$\frac{x^2+4}{x}+x=45$

Now, we solve for x

$\begin{gathered} \frac{x^2+4+x^2}{x}=45 \\ 2x^2+4=45x \\ 2x^2-45x+4=0 \end{gathered}$

Using a calculator, the solutions are 22.41 and 0.09. This means Max has 22 apples in total, because 22.41 is an incomplete number, so we have to round to the whole number.

Therefore, Max has 22 apples.