How to find a ratio

Help Questions

ISEE Middle Level Quantitative Reasoning › How to find a ratio

Questions 1 - 10

In February, there were 12 rainy days, 6 cloudy days and 10 sunny days. What was the ratio of sunny days in February?

Explanation

Identify the number of sunny days in February :

Then, creating a ratio, show the number of sunny days compared to the total number of days in the month of February (28):

Answer:

In a bowl of pieces of fruit, $\frac{2}{3}$ are apples. The rest are kiwis. If the number of apples is doubled, what is the ratio of kiwis to the total number of fruit in the newly enlarged quantity of fruit in the bowl.

Explanation

We know that $\frac{2}{3}$ of the total pieces of fruit are apples. This means that there are:

$\frac{2}{3} * 45 = 30$ apples.

Thus far, we know that we must have:

apples

and

kiwis

Now, if we double the apples, we will have:

apples

and

kiwis

This means that the proportion of kiwis to total fruit will be:

or , which can be reduced to

$\frac{M}{6} = \frac{N}{7}$

and are positive. Which is the greater quantity?

(a)

(b)

(b) is the greater quantity

(a) is the greater quantity

It is impossible to determine which is greater from the information given

(a) and (b) are equal

Explanation

The cross products of two equivalent fractions are themselves equivalent, so if

$\frac{M}{6} = \frac{N}{7}$

then

Multiply by 6:

$6 \cdot 6N=6 \cdot 7 M$

Since , it follows that , and by substitution,

Mike drove 120 miles to his mother's house. He finished the trip in two hours and 15 minutes. It took him one hour to drive the first 50 miles.

Which is the greater quantity?

(a) Mike's average speed over the first 50 miles

(b) Mike's average speed over the last 70 miles

(b) is greater

(a) is greater

(a) and (b) are equal

It is impossible to tell from the information given

Explanation

We can compare miles per hour.

(a) 50 miles over a one-hour period is 50 miles per hour.

(b) 70 miles over a one-and-one-fourth-hour period is

$70 \div 1\frac{1}{4} = \frac{70}{1} \div \frac{5}{4} = \frac{70}{1} \times \frac{4}{5} = \frac{14}{1} \times \frac{4}{1} = 56$

Mike drove an average of 56 miles per hour over the last 70 miles, making (b) greater.

In a given neighborhood, there are 200 vehicles. Half of these are cars, a quarter are SUVs, five percent are motorcycles, and the remaining amount are trucks. If the number of trucks are doubled, what is the ratio of motorcycles to total vehicles?

Explanation

You just need to work this through step-by-step.

We know that half of the vehicles are cars; therefore, of them are cars. To find the number of SUVs, multiply by (a quarter) and get SUVs. To find the number of motorcycles, multiply by to get . Finally, there is % remaining for trucks; therefore, multiply by to get .

Now, if this is doubled, we have trucks. This means that the total number of vehicles is:

vehicles

Therefore, the ratio of motorcycles to total vehicles will be:

Reducing this, you get:

If you want to share a pizza with your friend with a ratio of with you getting part and your friend getting parts, how much pizza does your friend get if there are slices of pizza?

Explanation

If the ratio is , there are total parts.

That means your friend get out of parts or $\frac{3}{4}$ .

If a pizza has slices, that means that your friend's number of slices is $\frac{3}{4}$ of or slices.

and are positive.

The ratios 20 to and to 40 are equvalent.

Which is the greater quantity?

(a)

(b)

It is impossible to determine which is greater from the information given

(a) is the greater quantity

(b) is the greater quantity

(a) and (b) are equal

Explanation

The ratios 20 to and to 40 are equvalent, so

$\frac{20}{M} = \frac{N }{40}$

By the cross-product property,

$MN = 20 \cdot 40 = 800$

Without any futher information, however, it cannot be determined which of and is the greater. For example, and fits the condition, as does the reverse case.

Sharon is having a birthday party. So far, she has invited twenty of her friends from school, nine of whom are girls. She wants to make the ratio of boys to girls at the party two to one. If she decides to add her two cousins, both boys, to the guest list, and no other girls, how many more boys does she need to invite?

Explanation

So far, Sharon has invited twenty friends from school - eleven boys and nine girls. Including Sharon's cousins and Sharon herself, there are thirteen boys and ten girls.

For there to be a two-to-one boy-to-girl ratio, Sharon must have twice as many boys as girls. She will need $10 \times 2 = 20$ boys total, so she will need to invite more boys.