Question

1. A hat store tracks the state of college and professional team hats for m, months. The number of
college hats sold is represented by (6m+3). The number of professional hats sold is represented by
(5m-2). Write an expressions to show how many more college hats were sold than professional hats.
Then evaluate the expression if m equals 10.
NYS
2. Which expression is equivalents to the expression -3(4x-2)-
2x ? Explain the process you used to find your solution.
A. -8x
B. -16%
C. -14x-2
D. -14x + 6
3. A square scrapbooking page has a perimeter of (8x+20) inches. What is the length of one side of the
scrapbooking page? Show your work.

Answer 1

1)  The expression representing how many more college hats were sold than professional hats is $m+5$

when  $m=10$, $15$ more college hats were sold

2)  The equivalent expression to $-3(4x-2)-2x$ is $-14x+6$. The explanation is found in the steps below

3) The length of one side of the square scrapbooking page will be

$(2x+5)\text{ inches}$. The working is shown below.

1)    According to the question, $m$ is the number of months hats were sold.

$6m+3$ is the number of college hats sold in $m$ months

$5m-2$ is the number of professional hats sold in $m$ months

Since $6m+3>5m-2$ when $m>0$

the expression representing how many more college hats were sold than professional hats is

$(6m+3)-(5m-2)\\=6m+3-5m+2\\=m+5$

when the number of months hats were sold is $10$, $m=10$, and

$m+5=(10)+5=15hats$

$15$ more college hats were sold in $10$ months

2)  To get the equivalent expression to $-3(4x-2)-2x$, carry out the steps below

remove brackets

$-12x+6-2x$

arrange like terms

$-12x-2x+6$

simplify like terms

$-14x+6$

The answer is (D)

3)  Let the length of one side of the square be $s$

The perimeter will be  

$4s=8x+20$

making $s$ the subject of the formula

$\dfrac{4s}{4}=\dfrac{8x+20}{4}\\\\s=(2x+5)\text{ inches}$

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