Show work: this is for my daughter in 7th. grade; needed some insight 15 points, and brainliest to whom show work with correct answers!

1a - a boat travel 468 kilometers on 117 liters of gasoline. how much gasoline will it need to go 168 kilometers

1b: a car travels 138 miles in 4 hours (with constant speed) how far can it travel in 10 hours (with the same speed)

2a: a boat travels 261 miles in 15 hours (with a constant speed) how much time will it take traveling 180 miles?

2b: a car travels 452 km. in 5 hours (with a constant speed) how far can it travel in 4 hours?

5a: 50 lbs. of tomatoes cost $200. how much would 2 lbs cost?

5b: a boat travels 381 km. in 6 hours (with a constant speed) how far can it travel in 7 hours (with the same speed)?

5c: a boat travels 427 km. in 43 hours (with constant speed) how much time will it take traveling 459 kilometers?

5d: 11 kg. of bananas cost $88 how much would 20 kg cost?

-p-

1a. 42 liters

1b. 345 miles

2a. 10 h 20 min 41.4 sec

2b. 361.6 km

5a. $8

5b. 444.5 km

5c. 46 h 13 min 20.9 sec

5d. $160

Step-by-step explanation:

Each of these problems expresses a proportion and asks you to find a missing value. You are given, for example, value 1 and related value 1. You are asked to find value 2 that corresponds to related value 2.

Solving the Proportion

Expressed as a proportion, this looks like ...

... (value 1)/(related value 1) = (value 2)/(related value 2)

If you multiply both sides of this equation by related value 2, you can find value 2.

... (related value 2)/(related value 1)×(value 1) = value 2

Another way to think about it

I like to think of the related values as making a fraction. If the related value 2 is larger than related value 1, the fraction is greater than 1 and the value 2 will be larger than value 1. (This realization can serve as a check on your answer.)

1a. related value 2 = 168 km. This is the value for which you want to find value 2, the number of liters of gasoline. related value 1 has the same units as related value 2 (km), and value 1 has the same units as value 2 (liters).

Then the fraction of interest is (168 km)/(468 km), and it multiplies 117 L. The result is ...

... (168/468)×(117 L) = 42 L

1b. (10 h)/(4 h)×(138 mi) = 345 mi

2a. (180 mi)/(261 mi)×(15 h) ≈ 10.3448 h

2b. (4 h)/(5 h)×(452 km) = 362.6 km

You may have noticed that I keep the units with the numbers. When the same units are in the numerator and denominator, they cancel—the way any common factors cancel. The remaining units will be the units of the answer. This practice of keeping units with numbers can help ensure you're using the right numbers for the right purpose. If the units don't work out, your math has an error.

5a. (2 lb)/(50 lb)×$200 = $8

5b. (7 h)/(6 h)×381 km = 444.5 km

5c. (459 km)/(427 km)×(43 h) ≈ 46.2225 h

5d. (20 kg)/(11 kg)×$88 = $160

600,000,000,000, or 6e14

step-by-step explanation: