ISEE Lower Level Quantitative Reasoning - How to find the solution to an equation

Five more than a number is equal to $\frac{3}{5}$ of twenty-five . What is the number?

Explanation

From the question, we know that plus a number equals $\frac{3}{5}$ of . In order to find out what $\frac{3}{5}$ of is, multiply $\frac{3}{5}$ by $\frac{25}{1}$ .

$\frac{3}{5}\times\frac{25}{1}=\frac{75}{5}$ , or .

The number we are looking for needs to be five less than , or .

You can also solve this algebraically by setting up this equation and solving:

$5+x=\frac{3}{5}\times25$

Subtract from both sides of the equation.

4 puppies from a litter are adopted, and $\frac{1}{3}$ are not adopted. How many puppies are in the litter?

Explanation

If $\frac{1}{3}$ are not adopted, then $\frac{2}{3}$ are adopted. We also know that the number of adopted puppies is 4.

Set up a proportion and solve:

$\frac{4}{x}=\frac{2}{3}$

Therefore, there are 6 puppies total in the litter.

What is the value of in the equation below?

Explanation

In order to solve for in , add 4.65 to each side of the equation.

This results in:

At a local market, farmers trade produce to obtain a more diverse crop. A farmer will trade turnips for ears of corn. If a man has ears of corn, then how many turnips can he get?

$351\ \text{turnips}$

$153\ \text{turnips}$

$531\ \text{turnips}$

$353\ \text{turnips}$

$533\ \text{turnips}$

Explanation

Ratios can be written in the following format:

$A:B\rightarrow \frac{A}{B}$

Using this format, substitute the given information to create a ratio.

$3\ \text{corn}: 13\ \text{turnips}$

Rewrite the ratio as a fraction.

$3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$

We know that the farmer has ears of corn. Create a ratio with the variable that represents how many turnips he can get.

$\frac{81\ \text{corn}}{T}$

Create a proportion using the two ratios.

$\frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{81\ \text{corn}}{T}$

Cross multiply and solve for .

$81\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$

Simplify.

Divide both sides of the equation by .

$\frac{3T}{3}=\frac{1053}{3}$

Solve.

The farmer can get $351\ \text{turnips}$ .

What is the value of h in the expression below?

Explanation

The steps for solving the equation, are below:

First, multiply 3 by the components of the parentheses.

Subtract 12 from each side.

Divide each side by 15.

At a local market, farmers trade produce to obtain a more diverse crop. A farmer will trade turnips for ears of corn. If a man has ears of corn, then how many turnips can he get?

$39\ \text{turnips}$

$93\ \text{turnips}$

$94\ \text{turnips}$

$43\ \text{turnips}$

$22\ \text{turnips}$

Explanation

Ratios can be written in the following format:

$A:B\rightarrow \frac{A}{B}$

Using this format, substitute the given information to create a ratio.

$3\ \text{corn}: 13\ \text{turnips}$

Rewrite the ratio as a fraction.

$3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$

We know that the farmer has ears of corn. Create a ratio with the variable that represents how many turnips he can get.

$\frac{9\ \text{corn}}{T}$

Create a proportion using the two ratios.

$\frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{9\ \text{corn}}{T}$

Cross multiply and solve for .

$9\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$

Simplify.

Divide both sides of the equation by .

$\frac{3T}{3}=\frac{117}{3}$

Solve.

The farmer can get $39\ \text{turnips}$ .

At a local market, farmers trade produce to obtain a more diverse crop. A farmer will trade turnips for ears of corn. If a man has ears of corn, then how many turnips can he get?

$650\ \text{turnips}$

$750\ \text{turnips}$

$560\ \text{turnips}$

$550\ \text{turnips}$

$860\ \text{turnips}$

Explanation

Ratios can be written in the following format:

$A:B\rightarrow \frac{A}{B}$

Using this format, substitute the given information to create a ratio.

$3\ \text{corn}: 13\ \text{turnips}$

Rewrite the ratio as a fraction.

$3\ \text{corn}: 13\ \text{turnips}\rightarrow \frac{3\ \text{corn}}{13\ \text{turnips}}$

We know that the farmer has ears of corn. Create a ratio with the variable that represents how many turnips he can get.

$\frac{150\ \text{corn}}{T}$

Create a proportion using the two ratios.

$\frac{3\ \text{corn}}{13\ \text{turnips}}=\frac{150\ \text{corn}}{T}$

Cross multiply and solve for .

$150\ \text{corn}\times 13\ \text{turnips}=3\ \text{corn}\times T$

Simplify.

Divide both sides of the equation by .

$\frac{3T}{3}=\frac{1950}{3}$

Solve.

The farmer can get $650\ \text{turnips}$ .

At a local market, farmers trade produce to obtain a more diverse crop. A farmer will trade turnips for ears of corn. If a man has ears of corn, then how many turnips can he get?