(a) If the team won 98 games, they lost 64 games. So the ratio of wins to losses is 98 : 64, or 98/64.

(b) The ratio of wins to games is 98/162.

(a) Juice that is 1/5 concentrate means that the total amount of juice is 5. One part of that total 5 is concentrate. The amount of water is total juice minus concentrate, so 5 – 1 = 4. The ratio of concentrate to water is 1 : 4.

(b) The fraction of concentrate in the total amount of juice is 1/5. Water makes up the rest of the juice, so its fraction is 4/5.

Write the ratio of the two numbers x to y as x/y = 4/1 , so x = 4y

Their sum is 40, so x + y = 40.

4y + y = 40 Substitute x = 4y into x + y = 40
5y = 40
y = 8

x = 4y, so x = 32

The two numbers are 32 and 8.

Use the total number of marbles in the bag and the ratio of just blue plus yellow.

blue + yellow = marbles left
2x + 6x = 32
8x = 32, so x = 4.

You can use x = 4 and the original 5 : 2 : 6 ratio to find the number of red marbles.
5x = 5 × 4 = 20
There were 20 red marbles in the bag.

The correct answer choice is (C).

Make sure you’re answering the question being asked. Here, the wrong answer options include x = 4, 2x = 8 blue marbles, 6x = 24 yellow marbles, and 32 + 20 = 52 marbles originally in the bag.

Method 1

35 × 24 = 84x Cross multiply.

x = 35 × 24 /84 Divide both sides by 84.

x = 35 × 24/84 = 7 × 5 × 2 × 2 × 6/2 × 6 × 7 = 10 Factor and cancel to simplify the calculations.

x = 10

Method 2

35/84 = x/24 Factor and simplify the fractions.

7 × 5/7 × 12 = x/2 × 12
5/12 = x / (2 × 12)
5 = x / 2
x = 10

Write the proportion using fractions.

4/15 = 16/x

4x = 16 × 15 Cross multiply.

x = 16 × 15/4 = 4 × 15 = 60 Divide both sides by 4.
x = 60

Write the question as a proportion.

0.07/100 = g/10⁶

0.07 × 10⁶ = 100g Cross multiply.

g = (0.07 × 10² × 10⁴)/100 = (7 × 10⁴)/10²= 7 × 10² Divide both sides by 100 and simplify.

g = 700

The correct answer choice is (C).

This represents a direct proportion: both the distance and time increase.

90 miles/1.5 hours = m/2.5 hours

m = 90 × 2.5/1.5 = 90 × 5 × 0.5/3 × 0.5 = 30 × 5 = 150

Roger would drive 150 miles.

This represents an indirect proportion: as the speed decreases, the time increases.

60 mph × 1 hour = 40 mph × h hours
60 = 40h

h = 60/40 = 1.5

It will take 1.5 hours. The speed is 40/60 = 2/3 of the original speed, so the time is 3/2 = 1.5 times the original time.

This represents an indirect proportion: as the number of workers increases, the time decreases.

4 men × 6 hours = 1 job
7 men × h hours = 1 job

Set the 2 equations equal.

4 × 6 = 7h
h = 24/7 = 3/3/7 ≈ 3.5

It will take the 7 men about 3.5 hours.