7th Grade Math - Solve Word Problems Leading to Equations: CCSS.Math.Content.7.EE.B.4a

If a rectangle possesses a width of $2\textup{ inches}$ and has a perimeter of $18\textup{ inches}$ , then what is the length?

$7\textup{ inches}$

$8\textup{ inches}$

$9\textup{ inches}$

$10\textup{ inches}$

$11\textup{ inches}$

Explanation

In order to solve this problem, we need to recall the formula for perimeter of a rectangle:

We can substitute in our known values and solve for our unknown variable (i.e. length):

We want to isolate the to one side of the equation. In order to do this, we will first subtract from both sides of the equation.

$\frac{\begin{array}[b]{r}18=2l+4\ -4\ \ \ \ \ \ -4\end{array}}{\\14=2l}$

Next, we can divide each side by

$\frac{\begin{array}[b]{r}\frac{14}{2}=\frac{2l}{2}\\end{array}}{7=l}$

The length of the rectangle is $7\textup{ inches}$

If a rectangle possesses a width of $8\textup{ inches}$ and has a perimeter of $36\textup{ inches}$ , then what is the length?

$10\textup{ inches}$

$11\textup{ inches}$

$12\textup{ inches}$

$13\textup{ inches}$

$14\textup{ inches}$

Explanation

In order to solve this problem, we need to recall the formula for perimeter of a rectangle:

We can substitute in our known values and solve for our unknown variable (i.e. length):

We want to isolate the to one side of the equation. In order to do this, we will first subtract from both sides of the equation.

$\frac{\begin{array}[b]{r}36=2l+16\ -16\ \ \ \ \ \ -16\end{array}}{\\20=2l}$

Next, we can divide each side by

$\frac{\begin{array}[b]{r}\frac{20}{2}=\frac{2l}{2}\\end{array}}{10=l}$

The length of the rectangle is $10\textup{ inches}$

If a rectangle possesses a width of $11\textup{ inches}$ and has a perimeter of $50\textup{ inches}$ , then what is the length?

$14\textup{ inches}$

$15\textup{ inches}$

$13\textup{ inches}$

$12\textup{ inches}$

$11\textup{ inches}$

Explanation

In order to solve this problem, we need to recall the formula for perimeter of a rectangle:

We can substitute in our known values and solve for our unknown variable (i.e. length):

We want to isolate the to one side of the equation. In order to do this, we will first subtract from both sides of the equation.

$\frac{\begin{array}[b]{r}50=2l+22\ -22\ \ \ \ \ \ -22\end{array}}{\\28=2l}$

Next, we can divide each side by

$\frac{\begin{array}[b]{r}\frac{28}{2}=\frac{2l}{2}\\end{array}}{14=l}$

The length of the rectangle is $14\textup{ inches}$

Gary is twice as old as his niece Candy. How old will Candy will be in five years when Gary is years old?

Not enough information is given to determine the answer.

Explanation

Since Gary will be 37 in five years, he is years old now. He is twice as old as Cathy, so she is $32 \div 2 =16$ years old, and in five years, she will be years old.

If a rectangle possesses a width of $12\textup{ inches}$ and has a perimeter of $36\textup{ inches}$ , then what is the length?

$6\textup{ inches}$

$5\textup{ inches}$

$7\textup{ inches}$

$8\textup{ inches}$

$9\textup{ inches}$

Explanation

In order to solve this problem, we need to recall the formula for perimeter of a rectangle:

We can substitute in our known values and solve for our unknown variable (i.e. length):

We want to isolate the to one side of the equation. In order to do this, we will first subtract from both sides of the equation.

$\frac{\begin{array}[b]{r}36=2l+24\ -24\ \ \ \ \ \ -24\end{array}}{\\12=2l}$

Next, we can divide each side by

$\frac{\begin{array}[b]{r}\frac{12}{2}=\frac{2l}{2}\\end{array}}{6=l}$

The length of the rectangle is $6\textup{ inches}$

If a rectangle possesses a width of $9\textup{ inches}$ and has a perimeter of $48\textup{ inches}$ , then what is the length?

$15\textup{ inches}$

$16\textup{ inches}$

$17\textup{ inches}$

$14\textup{ inches}$

$13\textup{ inches}$

Explanation

In order to solve this problem, we need to recall the formula for perimeter of a rectangle:

We can substitute in our known values and solve for our unknown variable (i.e. length):

We want to isolate the to one side of the equation. In order to do this, we will first subtract from both sides of the equation.

$\frac{\begin{array}[b]{r}48=2l+18\ -18\ \ \ \ \ \ -18\end{array}}{\\30=2l}$

Next, we can divide each side by

$\frac{\begin{array}[b]{r}\frac{30}{2}=\frac{2l}{2}\\end{array}}{15=l}$

The length of the rectangle is $15\textup{ inches}$

Let be the temperature expressed in degrees Celsius. Then the equivalent temperature in degrees Fahrenheit can be calculated using the formula:

$F = \frac{9}{5} C + 32$

What is $65^{\circ } C$ expressed in degrees Fahrenheit?

$149 ^{\circ } F$

$174.6^{\circ } F$

$59.4^{\circ } F$

$85 ^{\circ } F$

Explanation

$F = \frac{9}{5} C + 32$

$F = \frac{9}{5} \cdot 65 + 32 = 117+32 = 149 ^{\circ } F$

Let be the temperature expressed in degrees Fahrenheit. Then the equivalent temperature in degrees Celsius can be calculated using the formula:

$C = \frac{5}{9} (F-32)$

What is $80^{\circ } F$ expressed in degrees Celsius (to the nearest degree)?

$27^{\circ } C$

$12^{\circ } C$

$112^{\circ } C$

$87^{\circ } C$

Explanation

$C = \frac{5}{9} (F-32)$

$C = \frac{5}{9} (80-32)$

$C = \frac{5}{9} \cdot 48 \approx 26.7$ , which rounds to $27^{\circ } C$

Write as an equation:

Twice the sum of a number and ten is equal to the difference of the number and one half.

$2 (x+10) = x - \frac{1}{2}$

$2 (x+10) =\frac{1}{2} - x$

$2 x+10 = x - \frac{1}{2}$

$2 x+10 = \frac{1}{2} - x$

Explanation

Let represent the unknown number.

"The sum of a number and ten" is the expression . "Twice" this sum is two times this expression, or

"The difference of the number and one half" is a subtraction of the two, or

$x - \frac{1}{2}$

Set these equal, and the desired equation is

$2 (x+10) = x - \frac{1}{2}$

Write as an equation:

Five-sevenths of the difference of a number and nine is equal to forty.

$\frac{5}{7} (y- 9) = 40$

$\frac{5}{7} y- 9 = 40$

$\frac{5}{7} (9 - y) = 40$

$9 - \frac{5}{7} y = 40$

Explanation

"The difference of a number and nine" is the result of a subtraction of the two, so we write this as

"Five-sevenths of" this difference is the product of $\frac{5}{7}$ and this, or

$\frac{5}{7} (y- 9)$

This is equal to forty, so write the equation as

$\frac{5}{7} (y- 9) = 40$

Solve Word Problems Leading to Equations: CCSS.Math.Content.7.EE.B.4a

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