Algebraic Concepts

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ISEE Lower Level Quantitative Reasoning › Algebraic Concepts

Questions 1 - 10

The toy panda weighs pounds less than the toy truck. The toy truck weighs pounds. Select the number sentence that gives the weight of the toy panda.

Explanation

We are told that the toy panda weighs pounds less than the toy truck, which means we are going to subtract.

We are given that the toy truck weighs pounds, so we subtract from since the panda weighs pounds less than the toy truck.

is the correct number sentence.

What is the value of in the equation below?

Explanation

To solve, you will need to divide both sides of the equation by 5.

$\frac{5y}{5}=\frac{25}{5}$

The 5 cancels on the left side.

$y=\frac{25}{5}$

Divide to simplify.

What is the value of in the equation below?

Explanation

To solve, you will need to divide both sides of the equation by 5.

$\frac{5y}{5}=\frac{25}{5}$

The 5 cancels on the left side.

$y=\frac{25}{5}$

Divide to simplify.

If $\small y=5$ , which of the following number sentences are true?

$\small 2\left ( y-2\right )=6$

$\small 3y-6=19$

$\small 5\left ( y+4\right )=42$

$\small 4y+7=20$

Explanation

Replace the variable $\small y$ with $\small 5$ . Then solve using order of operation (PEMDAS).

$\small 2\left ( y-2\right )=6$

$\small 2\left ( 5-2\right )=6$

$\small 5-2=3$

$\small 2\times3=6$

If and , what is ?

Explanation

Sometimes we use letters instead of numbers if we don't know what number ought to go in a certain place. Saying "" means that something plus eight equals fifteen, but we aren't yet certain what that "something" is. When we can, we solve the puzzle of what number that letter could be replaced with.

. , so must be replaced by .

. , so must be replaced by also.

We're looking for . To find this, we replace the letters with the numbers we found. and both equal , so .

, so . The correct answer is .

If and , what is ?

Explanation

. , so must be replaced by .

. , so must be replaced by also.

We're looking for . To find this, we replace the letters with the numbers we found. and both equal , so .

, so . The correct answer is .

If $\small y=5$ , which of the following number sentences are true?

$\small 2\left ( y-2\right )=6$

$\small 3y-6=19$

$\small 5\left ( y+4\right )=42$

$\small 4y+7=20$

Explanation

Replace the variable $\small y$ with $\small 5$ . Then solve using order of operation (PEMDAS).

$\small 2\left ( y-2\right )=6$

$\small 2\left ( 5-2\right )=6$

$\small 5-2=3$

$\small 2\times3=6$

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?