Mass Of 3 pineapples and 2 apples is 11.4 kg. Total mass of 2 pineapples and 4 apples is 8.4 kg. Find the mass of 1 pineapple and 1 apple.

Question

Help needed as this is creating problem for my kid.

Answer 1

Let's call pineapples p and apples a.

So we have two equations and two variables.

Equation 1: 3p + 2a = 11.4

Equation 2: 2p + 4a = 8.4

There are several ways to solve 2 variable equation. Here I'll demonstrate the substitution method.

Pick one variable to isolate. I'll use 'a'. Take one of the equations (either one works).

2p + 4a = 8.4

Use algebra to solve for a. (Isolate it by itself on one side of the equation).

Subtract 2p from both sides

4a = 8.4 - 2p

Divide both sides by 4

a = 2.1 - 0.5p

Now use that equation for 'a' and substitute it for 'a' in Equation 1. (use the equation you didn't in step 1)

3p + 2(2.1 - 0.5p) = 11.4

Now you notice we have an equation with just the 'p' variable.

Use algebra to solve from there.

3p + 4.2 - p = 11.4

2p + 4.2 = 11.4

2p = 7.2

p= 3.6

Since we used both equations we now have a real value for the weight of a pineapple: 3.6 kg.

We can use that answer and plug it back into our equation for 'a'.

a = 2.1 - 0.5p

a = 2.1 - 0.5(3.6)

a=1.2

Now we have a real value for weight of an apple: 0.3 kg.

To confirm we have the right answer we can double check from the original problem.

3(3.6) + 2(0.3) = 11.4

10.8 + 0.6 = 11.4

11.4 = 11.4

Since this is true we know that the weights we found are correct.