Question

A fruit company delivers its fruit in two types of boxes: large and small. A delivery of
3 large boxes and
5 small boxes has a total weight of
116 kilograms. A delivery of
9 large boxes and
7 small boxes has a total weight of
238 kilograms. How much does each type of box weigh?

Answer 1

Answer:

Small box weighs 13.75 kg & large box weighs 15.75 kg

Step-by-step explanation:

We can write 2 simultaneous equation and solve for weight of each box.

Let weight of large box be l and small box be s.

"3 large boxes and  5 small boxes has a total weight of  116 kilograms":

$3l+5s=116$

and

"9 large boxes and  7 small boxes has a total weight of  238 kilograms":

$9l+7s=238$

Now we can solve for l in the 1st equation and put it into 2nd equation and get s:

$3l+5s=116\\3l=116-5s\\l=\frac{116-5s}{3}$

now,

$9l+7s=238\\9(\frac{116-5s}{3})+7s=238\\3(116-5s)+7s=238\\348-15s+7s=238\\348-238=15s-7s\\110=8s\\s=\frac{110}{8}=13.75$

now we plug in 13.75 into s into equation of l to find s:

$l=\frac{116-5s}{3}\\l=\frac{116-5(13.75)}{3}\\l=15.75$