A delivery truck is transporting boxes of two sizes: large and small. The large boxes weigh 60 pounds each, and the small boxes weigh 20 pounds each. There are 125 boxes in all. If the truck is carrying a total of 4700 pounds in boxes, how many of each type of box is it carrying?

Answers

Answer 1

Answer:

Answer:

55 large boxes and 70 small boxes

Step-by-step explanation:

We understand that there are two unknowns in this problem: the number of large boxes and the number of small boxes.

Let's identify with the letter L the number of large boxes that are transported, and with the letter S the number of small boxes, so we can easily identify the unknowns when writing and reading our equations and final answers.

Set up two equations:

1) one for the total weight of the boxes being transported (which should add up to 4700 pounds), and considering that we have "L" number of large boxes (each one 60 pound weight), and "S" number of boxes (each one 20 pound weight):

60 * L + 20 * S = 4700

2) another equation for the total number of boxes (125) which should be addition of L large boxes and S small ones:

L + S = 125

Now solve for one of the unknowns (let's say for example "S") in the easy second equation we wrote:

S = 125 - L

Now use this expression for "S" (to replace it in terms of L) in the first (more complex) equation:

60 * L + 20 * (125-L) = 4700

Now apply distributive property to remove the parenthesis on the second term on the left of the equation:

60 * L + 2500 - 20 * L = 4700

subtract 2500 from both sides (to group all numerical terms on the right hand side):

60 * L - 20 * L = 4700-2500= 2200

combine the like terms 60L and -20L:

40 * L = 2200

now divide both sides by 40 to solve for L

therefore: L = 2200 / 40 = 55

There are 55 large boxes.

Now to find the number of small boxes, we use this result: "L=55" in the second (simple/easy) equation we created:

S = 125 - L = 70

Therefore, there are 70 small boxes.

2.5 gallons are equal to 10 quarts.

Step-by-step explanation:

We know that 1 gallon is equivalent to 4 quarts.

Let's call $g$ gallons and $q$ quarts. An expression that represents the transformation between these two units is

$q=4g$

This expression represents the conversion factor we described at the beginning.

So, if we have 2.5 gallons, using the expression, we find the number of quarts

$q=4(2.5)\nq=10$

Therefore, 2.5 gallons are equal to 10 quarts.

The expression 2.5 gallons x 4 quarts/gallon can be used to convert 2.5 gallons into quarts.

We have,

To convert 2.5 gallons into quarts, you can use the conversion factor that states there are 4 quarts in 1 gallon.

The expression to convert 2.5 gallons into quarts would be:

2.5 gallons x 4 quarts/gallon

By multiplying 2.5 gallons by the conversion factor of 4 quarts/gallon, you would obtain the equivalent value in quarts.

Thus,

The expression 2.5 gallons x 4 quarts/gallon can be used to convert 2.5 gallons into quarts.

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An angle measures 56° less than the measure of a complementary angle. What is the measure of each angle?

Answers

Well, firstly a complementary angle is 90 degrees.
if an angle measures 56 degrees less than 90 degrees that means that it is 90- 56= 34
so, therefore the measure of each angle is 34 degrees.

Final answer:

To find the measure of each angle, assume the measure of one angle is x degrees. The other angle measures 56° less than the measure of its complementary angle. Solve the equation to find the measures of the angles.

Explanation:

To find the measure of each angle, let's assume the measure of one angle is x degrees.

According to the problem, the other angle measures 56° less than the measure of its complementary angle, which means it is 90 - x - 56 = 34 - x degrees.

Since two angles are complementary, their sum should be equal to 90 degrees.

Therefore, x + (34 - x) = 90.

Solving the equation, we get x = 28 degrees and 34 - x = 34 - 28 = 6 degrees.

So, the measure of each angle is 28 degrees and 6 degrees, respectively.

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Please help me with this

Answers

Tony found about 30 worms. It's a bit over 25, so I concluded 35. Gemma found more snails. She found about 50 Snails. I know this because the chart it halfway full of snails. Hope this helps!

Harrison worked on his solar system project 5 hours each week for 2 week how many hours did he work on his project