Question

3. A crate with 20 bricks weighs 167 pounds. When the same crate has 32 bricks, it weighs
191 pounds. How much would the crate weigh if there were 19 bricks in the crate?
Explain.

Answer 1

The weight of crate when it has 19 bricks is 165 pounds

Solution:

Given that, A crate with 20 bricks weighs 167 pounds.  

When the same crate has 32 bricks, it weighs 191 pounds.  

Now, let the weight of each brick be "m" pounds and weight of the crate be 'n" pounds.

Then, when crate has 20 bricks

Total weight = weight of bricks + weight of crate

$167 \text { pounds }=\text { number of bricks } \times \text { weight of each brick }+\text { weight of crate }$

$167=20 \times m+n$

20m + n = 167 ----- eqn (1)

Now, when crate has 32 bricks

Total weight = weight of bricks + weight of crate

$191 \text { pounds }=\text { number of bricks } \times \text { weight of each brick + weight of crate }$

$191=32 \times m+n$

32m + n = 191 ----- eqn (2)

Now, subtract (1) from (2)

32m + n = 191

20m + n = 167

(-) ----------------

12m + 0 = 24

m = 2

Then, from eqn (1)  

20(2) + n = 167  

40 + n = 167  

n = 167 – 40 = 127

Now, when the box has 19 bricks

Total weight = 19 bricks x 2 pounds per brick + 127 pounds of crate

$\text { Total weight }=19 \times 2+127=38+127=165$

Hence, the weight of crate when it has 19 bricks is 165 pounds.