# Tania bought 4 more pounds of pears than Wilma. Together, Tania and Wilma bought 18 pounds of pears. How many pounds of pears did Wilma buy?

Mar 1, 2018

Wilma bought 7 pounds of pears.

#### Explanation:

Let pounds bought by Wilma be $x$.
Then those bought by Tania will be $x + 4$

So we have:

$x + x + 4 = 18$
$2 x + 4 = 18$
$2 x = 14$
$x = 7$

So Wilma bought 7 pounds of pears.

Mar 1, 2018

Tanya has $11$ pounds of pears
Wilma has $7$ pounds of pears

#### Explanation:

Let Tania's pounds of pears be $t$

Let Wilma's pounds of pears $w$

The first sentence, "Tania bought 4 more pounds of pears than Wilma" can be written as:

$t = w + 4$

The second sentence, "Tania bought 4 more pounds of pears than Wilma" can be written as:

$t + w = 18$

So, the two equations we have are:

$t = w + 4$
$t + w = 18$

Multiply the second equation by $- 1$

$t = w + 4$

$- t - w = - 18$

Now, we add both the simultaneous equations:

$\left(t\right) + \left(- t\right) + \left(- w\right) = \left(4\right) + \left(- 18\right) + \left(w\right)$

$t - t - w = 4 - 18 + w$

$t$ and $- t$ cancel out:

$- w = - 14 + w$

$- 2 w = - 14$

$2 w = 14$

$w = 7$

Now that we have one variable, we can substitute it inside any one of the equations. Let us take the first equation, as $t$ is alone, and it would be easier to manipulate it:

$t = w + 4$

Since $w = 7$:

$t = 7 + 4$

$t = 11$

Thus, Tanya has $11$ pounds of pears.
Thus, Wilma has $7$ pounds of pears