Q5: Ratios

Question 1

For every 5 men, there are 3 women.

Express the above ratio in 3 different ways

Answer 1

Question 2

If there are 25% more women than men, what is the ratio of men to women?

Answer 2

Question 3

If the ratio of men to women is 5:7, what fraction of the total are women?

Answer 3

Question 4

If the ratio of men to women is 3:4, which of the following could NOT be the total number of men and women combined?

A) 35

B) 72

C) 49

D) 21

E) 280

Answer 4

We can’t have a fraction of a person.

Therefore, the total must be a multiple of 7. (3+4)

7, 14, 21, 28, etc.

Only B is not a multiple of 7. (we might notice that 70 is a multiple of 7, so 72 isn’t)

35= 5*7

49=7*7

21= 3*7

280= 40*7

Question 5

If the ratio of flour to water in a recipe is 3:2, how many cups of flour would we need for 7 cups of water?

Answer 5

Unlike for people, We CAN have fractions of units.

We can use the Unknown Multiplier method:

The ratio of flour to water is 3x : 2x, with x as our unknown multiplier.

We know the amount of water, 7, so 2x=7.

Solve for x: x=3.5

Now plug in x=3.5 and find the flour:

3x = 3*3.5 = 10.5 cups of flour

Question 6

There are 20% more men than women. If there are 66 people, how many are women?

Answer 6

M = 1.2W

M = (6/5) W

Ratio of men to women = 6:5

Use unknown multiplier: 6x:5x

The total men and women are 66, so 6x + 5x = 66

11x = 66

x = 6. Then we need to plug back in to our ratio. Women are 5x, so 5*6 = 30

Question 7

If the ratio of dogs to cats to birds is 2:3:5, and there are 24 cats, how many total animals are there?

Answer 7

We can use the unknown multiplier:

2x:3x:5x

3x represents cats. 3x=24

x=8

So, our multiplier is 8.

Counting all 3 animals, we have 2x+3x+5x = 10x

So, 10x = 10*8 = 80

Question 8

There are 3x for every 2y.

There are 3z for every 5x

What is the ratio of y to z?

Answer 8

ratio 1) 3x:2y

ratio 2) 3z:5x

We use a similar process to finding a common denominator with fractions:

What is the common factor between 3x and 5x? 15x

Multiply the 1st ratio by 5: 15x:10y

Multiply the 2nd ratio by 3: 9z:15x

So, for every 15x there is 10y, and 9z

Therefore the ratio of y to z is 10:9

Question 9

What is the definition of “directly proportional”?

Answer 9

When 2 quantites vary by a constant ratio.

It is a linear relationship: y = mx, where m is the slope or constant ratio The graph would start at 0,0

examples: someone earns $20 per hour, with no other payments.