Answer:
The values of each of the small boxes are 6.5 kilograms and for the large boxes 15.5 kilograms.
Explanation:
Make variables to represent each of the boxes, small and large.
Small box = x
Large box = y
Now, form an equation from each of the two statements they said.
We are given statement one:
A delivery of 2 large boxes and 12 small boxes equals to 109 kilograms.
We are also given statement two:
A delivery of 5 large boxes and 3 small boxes equals to 97 kilograms.
Make equations of both of these statements to represent that the sums of the boxes is equal to the amounts they gave:
Statement one's equation:
2y + 12x = 109, this shows that 2 of the large boxes (y) plus 12 of the small boxes (x) totals to 109 kilograms.
Statement two's equation:
5y + 3x = 97, this shows that 5 of the large boxes (y) plus 12 of the small boxes (x) totals to 97 kilograms.
Let's find out from either one equation of these two, the value of one certain box so we can later plug this value into either equation.
Let's find statement one's value. In order to do this, you can decide whether to solve for the value of the large box or the value of the small box. I'll choose to find the value of the small box so we can later plug the value of the small box's value into either equation like I previously mentioned.
Statement one's equation:
2y + 12x = 109
To find the value of the small box, get "x" alone:
2y + 12x = 109
Subtract 2y from both sides since the inverse operation of addition is subtraction:
-2y -2y
12x = 109 - 2y
Divide both sides by 12 to get x alone since the inverse operation of multiplication is division:
/12 /12
x = 109/12 - 2/12y
Which simplifies to:
x = 109/12 - 1/6y.
Now, plug this value into either the original form of this equation OR the other equation, let's do the other:
Statement two's equation:
5y + 3x = 97
Substitute the value of the small box's value into this equation:
5y + 3(109/12 - 1/6y) = 97
5y + 27.25 - 1/2y = 97
Combine like terms:
4.5y + 27.25 = 97
Get rid of constants by using inverse operations:
-27.25 -27.25
4.5y = 69.75
y = 15.5 kilograms.
The weight/value of the large box is 15.5 kilograms.
Now, let's use this value and plug it into either equation again, let's use the same equation we used to solve for y:
5y + 3x = 97
Substitute:
5(15.5) + 3x = 97
Simplify:
77.5 + 3x = 97
Use inverse operations to get rid of constants:
-77.5 -77.5
3x = 19.5
Use inverse operations to get x alone:
x = 6.5 kilograms
The weight/value of the small box is 6.5 kilograms.
To double check, plug these values into the original equation to see if they work:
Use equations that we found:
2y + 12x = 109
and
5y + 3x = 97
Plug in values into the first equation:
2y + 12x = 109
2(15.5) + 12(6.5) = 109
31 + 78 = 109
109 = 109, this equation works.
Check into the other: (you really only need to check in one equation to prove they work)
Plug in values into the second equation:
5y + 3x = 97
5(15.5) + 3(6.5) = 97
77.5 + 19.5 = 97
97 = 97, this equation works.
Thus, the values of each of the small boxes are 6.5 kg and for the large boxes 15.5 kg.