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uranmaximum [27]
2 years ago
10

Two​ trains, Train A and Train​ B, weigh a total of 167 tons. Train A is heavier than Train B. The difference of their weights i

s 145 tons. What is the weight of each​ train?
Mathematics
1 answer:
Luba_88 [7]2 years ago
4 0

Answer:

Step-by-step explanation:

Two​ trains, Train A and Train​ B, weigh a total of 167 tons. Train A is heavier than Train B. The difference of their weights is 145 tons. What is the weight of each​ train?

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A publisher needs to send many books to a local book retailer and will send the books in a combination of small and large boxes.
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Answer:

5 large boxes

3 small boxes

Step-by-step explanation:

Create two equations to represent the problem.

let "a" be the number of small boxes

let "b" be the number of large boxes

20a + 40b = 260    This equation shows the numbers of books

a + b = 8                  This equations shows the number of boxes

Solve the system of equations (solve for a and b). We can solve using the substitution method.

Rearrange a + b = 8 to isolate one of the variables.

a = 8 - b    New equation that represents "a"

Since we know an equation for "a", we can substitute what "a" equals into the other equation. There will only be one variable in the equation, so we can solve by isolating. Isolate by doing reverse operations.

Substitute "a" for 8 - b

20a + 40b = 260

20(8 - b) + 40b = 260     Distribute 20 over the brackets by multiplying

160 - 20b + 40b = 260    Collect like terms (numbers with same variables)

160 + 20b = 260    Start isolating "b". Subtract 160 from both sides

20b = 260 - 160

20b = 100    Divide both sides by 20

b = 5    Number of large boxes

Substitute "b" for 5 in the simplest equation

a + b = 8

a + 5 = 8      Subtract 5 from both sides to isolate "a"

a = 8 - 5    

a = 3      Number of small boxes

Therefore there were 5 large boxes and 3 small boxes sent.

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