How to find a proportion

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ISEE Middle Level Quantitative Reasoning › How to find a proportion

Questions 1 - 10

If one cupcake costs 75 cents, how much does a dozen cupcakes cost?

Explanation

You can solve this problem using a proportion.

$\frac{1}{0.75}=\frac{12}{x}$

To solve for x, cross multiply.

$1\times x=12\times.75$

9 dollars

The distance between Carson and Miller is 260 miles and is represented by four inches on a map. The distance between Carson and Davis is 104 miles.

Which is the greater quantity?

(a) The distance between Carson and Davis on the map

(b) $1 \frac{1}{2} \textrm{ in}$

(a) is greater

(b) is greater

(a) and (b) are equal

It is impossible to tell from the information given

Explanation

Let be the map distance between Carson and Davis. A proportion statement can be set up relating map inches to real miles:

$\frac{N}{104} = \frac{4}{260}$

Solve for :

$\frac{N}{104} \cdot 104 = \frac{4}{260} \cdot 104$

$N = \frac{416}{260} = \frac{416\div 52 }{260\div 52} =\frac{8}{5} = 1\frac{3}{5}$

Carson and Davis are $1\frac{3}{5}$ inches apart on the map; $1\frac{3}{5} > 1 \frac{1}{2}$

A witch's brew contains newt eyes for every lizard tongues. If Aurelia the witch used newt eyes in her recipe, how many lizard tongues did she need to use?

Explanation

To solve this, you need to set up a proportion:

$\frac{18}{4} = \frac{x}{3}$

Multiply both sides by :

$x=\frac{54}{4}$

Simplifying, this gives you:

$\frac{27}{2}$ or lizard tongues.

The distance between Vandalia and Clark is 250 miles and is represented by six inches on a map. The distance between Vandalia and Ferrell is represented by three and three-fifths inches on a map.

Which is the greater quantity?

(a) The actual distance between Vandalia and Ferrell

(b) 150 miles

(a) and (b) are equal

(a) is greater

(b) is greater

It is impossible to tell from the information given

Explanation

Let be the real distance between Vandalia and Ferrell. A proportion statement can be set up relating real miles to map inches:

$\frac{N}{3 \frac{3}{5}} = \frac{250}{6}$

Solve for :

$\frac{N}{3 \frac{3}{5}} \cdot 3 \frac{3}{5} = \frac{250}{6}\cdot 3 \frac{3}{5}$

$N = \frac{250}{6}\cdot \frac{18}{5} = \frac{50}{1}\cdot \frac{3}{1} = 150$

The actual distance between Vandalia and Ferrell is 150 miles.

Isidore could buy equally-sized blocks of cheese for . How many could he buy for ?

Explanation

For this problem, set up a proportion:

$\frac{3}{48}=\frac{x}{192}$ , where represents the number of cheese blocks that Isidore can buy.

To solve this, multiply both sides by :

$\frac{192*3}{48}=x$

$\frac{576}{48}=x$

A given recipe calls for cups of butter for every cup of flower and cups of sugar. If you wish to triple the recipe, how many total cups of ingredients will you need?

Explanation

This is an easy case of proportions. To triple the recipe, you merely need to triple each of its component parts; therefore, you will have:

cups of butter for every cup of flower and cups of sugar

Summing these up, you get:

total cups.

If the ratio of boys to girls in a classroom is , and there are a total of of students in the classroom, how many boys are in the classroom?

Explanation

If the ratio of boys to girls in a classroom is , that means that there are boys for every girls. Thus, when there are students in a classroom, the breakdown will be boys and girls. If there are students in a classroom, the breakdown will be boys and girls, which translates to a ratio of , or .

Thus, if there are students, will be boys.

You survey students about the plans for a new practice court for the basketball team and they must give a yes or no answer. students are against the use of funds on this project. What proportion of students said that they agreed with the plan?

Explanation

If disagreed with the plan, that means the rest agreed.

So to find that value, you must do the total minus the no's

To find the proportion you must divide the part by the whole giving us an answer of

The distance between Youngston and Wynne is 240 miles in reality and three inches on a map. On the same map, Charlesville and Petersburg are one and three-fourths inches apart. How far apart are they in reality?

$140 \textrm{ mi}$

$120 \textrm{ mi}$

$128 \textrm{ mi}$

$144 \textrm{ mi}$

Explanation

240 real miles is represented by 3 map inches, making this a ratio of $240 \div 3 = 80$ real miles per map inch.

Therefore, one and three-fourths inches represents

$80 \times 1 \frac{3}{4} = \frac{80}{1} \times \frac{7}{4} = \frac{20}{1} \times \frac{7}{1} = 140$ miles, the distance between Charlesville and Petersburg.