A delivery truck is transporting boxes of two sizes: large and small. The combined weight of a large box and a small box is 70 pounds. The truck is transporting 50 large boxes and 70 small boxes. If the truck is carrying a total of 4100 pounds in boxes, how much does each type of box weigh?

Answers:

one small box = 30 pounds

one large box = 40 pounds

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Work Shown:

S+L = 70 since the two boxes combine to 70 pounds.

70S = weight of 70 small boxes

50L = weight of 50 large boxes

70S+50L = weight of 70 small and 50 large

70S+50L = 4100

The system of equations is

There are a few ways to solve this system. I'll use substitution.

I'm going to isolate L in the first equation like so

S+L = 70

L = 70-S

Which I'll then plug into the other equation to solve for S

70S+50L = 4100

70S+50(70-S) = 4100

70S+3500-50S = 4100

20S+3500 = 4100

20S = 4100-3500

20S = 600

S = 600/20

S = 30

Each small box is 30 pounds.

Use this value of S to find L

L = 70-S

L = 70-30

L = 40

Each large box is 40 pounds.

Like we expect, each large box weighs more compared to any given small box.

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Check:

Both equations are true for the ordered pair (S,L) = (30,40). Therefore, the answers have been confirmed.

c. 65°

step-by-step explanation:

we are given a triangle with two known angles, 62° and 53°, while the third angle x is unknown and we are to find its value.

we know that the sum of angles in a triangle is equal to a total of 180 degrees. so we can write it as:

x + 62° + 53° = 180°

solving to find the value of x:

x = 180 - (62 + 53) = 65°

therefore, the value of x in this triangle is 65°.

d

step-by-step explanation:

hello and welcome!

so, when we see the words "proportional" along with a table, we need to know that we're looking numbers that divide by the same thing.

looking at this table, we simply have to do a trial and error, and divide to see which numbers have the same quotient. if you look at choice a & c, they both have equal quotients for three of the numbers, with one exception, so those can't be the answer. looking at b, there is no similarity, so that can't be it. then, we see d; if you divide all the numbers in the table, you'll see that they all divide by two, which is a proportional relationship, and our answer!

also, always remember that the x will always be the number that goes into y, and somewhere behind this table, is a formula. for this specific table, the formula would be:

since our x-value is being divided by two to get the y-value. and if they were to ask for more numbers in the series, this is the formula you would use to find them.