Multi step equation

Question

There are two pear trees in Charles’s backyard. The height of the rst tree is two more than three times taller than the other. If the di€erence in height between the two trees is 14.5 feet, calculate the height of the shorter pear tree.

Answer 1

Lets call the first tree T₁ and the second tree T_2.

Set up an equation for each piece of information we know.

First, T₁ is equal to 2 more than 3 times T2.

In equation form, that means T₁ = 2 + 3*T₂ (3 times T2 and adding 2 more)

The problem also says the difference between T₁ and T_{2 is} 14.5.

We know T₁ is taller, because it is more than 3 times the height of T_2.

T₁ - T₂ = 14.5

We have 2 equations and 2 unknowns. Now we can solve.

The first equation says T₁ = 2 + 3*T₂ , so, we can plug that into the second equation where there is a T₁.

T₁ - T₂ = 14.5

(2 + 3*T₂₎ - T₂ = 14.5

solve for T₂.

2 + 2*T₂ = 14.5

2*T₂ = 12.5

T₂ = 6.25

To check:

This means T₁ is:

T₁ - 6.25 = 14.5

T₁ = 20.75

See if the first equation holds:

T₁ = 2 + 3*T₂

20.75 = 2 + 3(6.25)

20.75 = 2 + 18.75

20.75 = 20.75 √