MATH SOLVE

3 months ago

Q:
# 3. A crate with 20 bricks weighs 167 pounds. When the same crate has 32 bricks, it weighs191 pounds. How much would the crate weigh if there were 19 bricks in the crate?Explain.

Accepted Solution

A:

The weight of crate when it has 19 bricks is 165 poundsSolution: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[tex]167 \text { pounds }=\text { number of bricks } \times \text { weight of each brick }+\text { weight of crate }[/tex][tex]167=20 \times m+n[/tex]20m + n = 167 ----- eqn (1)Now, when crate has 32 bricks
Total weight = weight of bricks + weight of crate
[tex]191 \text { pounds }=\text { number of bricks } \times \text { weight of each brick + weight of crate }[/tex][tex]191=32 \times m+n[/tex] 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 bricksTotal weight = 19 bricks x 2 pounds per brick + 127 pounds of crate[tex]\text { Total weight }=19 \times 2+127=38+127=165[/tex] Hence, the weight of crate when it has 19 bricks is 165 pounds.