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ABC Bookstore sells new books, [tex]\(n\)[/tex], for [tex]\(\$12\)[/tex], used books, [tex]\(u\)[/tex], for [tex]\(\$8\)[/tex], and magazines, [tex]\(m\)[/tex], for [tex]\(\$5\)[/tex] each. The store earned [tex]\(\$340\)[/tex] revenue last month. The store sold 5 more used books than new books, and twice as many magazines as new books. Using the substitution method, how many magazines, new books, and used books did ABC Bookstore sell?

A. [tex]\(n=12\)[/tex]; [tex]\(u=8\)[/tex]; [tex]\(m=5\)[/tex]

B. [tex]\(n=15\)[/tex]; [tex]\(u=15\)[/tex]; [tex]\(m=10\)[/tex]

C. [tex]\(n=10\)[/tex]; [tex]\(u=15\)[/tex]; [tex]\(m=20\)[/tex]

D. [tex]\(n=20\)[/tex]; [tex]\(u=15\)[/tex]; [tex]\(m=10\)[/tex]



Answer :

GinnyAnswer
To solve this problem, let's start by defining the variables and the given information:

1. Let [tex]\( n \)[/tex] be the number of new books sold.
2. Let [tex]\( u \)[/tex] be the number of used books sold.
3. Let [tex]\( m \)[/tex] be the number of magazines sold.

The costs are:
- New books: \[tex]$12 each - Used books: \$[/tex]8 each
- Magazines: \[tex]$5 each The total revenue from these sales is \$[/tex]340:
[tex]\[ 12n + 8u + 5m = 340 \][/tex]

We are given two additional pieces of information:
1. The store sold 5 more used books than new books:
[tex]\[ u = n + 5 \][/tex]
2. The store sold twice as many magazines as new books:
[tex]\[ m = 2n \][/tex]

Now, using these relationships, let's substitute [tex]\( u \)[/tex] and [tex]\( m \)[/tex] in the revenue equation.

First, substitute [tex]\( u = n + 5 \)[/tex] and [tex]\( m = 2n \)[/tex] into the revenue equation:
[tex]\[ 12n + 8(n + 5) + 5(2n) = 340 \][/tex]

Next, distribute and combine like terms:
[tex]\[ 12n + 8n + 40 + 10n = 340 \][/tex]

Simplify the equation:
[tex]\[ 30n + 40 = 340 \][/tex]

To solve for [tex]\( n \)[/tex], subtract 40 from both sides:
[tex]\[ 30n = 300 \][/tex]

Then, divide both sides by 30:
[tex]\[ n = 10 \][/tex]

Now, using the value of [tex]\( n \)[/tex] to find [tex]\( u \)[/tex] and [tex]\( m \)[/tex]:

For [tex]\( u \)[/tex]:
[tex]\[ u = n + 5 = 10 + 5 = 15 \][/tex]

For [tex]\( m \)[/tex]:
[tex]\[ m = 2n = 2 \times 10 = 20 \][/tex]

Therefore, the bookstore sold:
- New books: [tex]\( n = 10 \)[/tex]
- Used books: [tex]\( u = 15 \)[/tex]
- Magazines: [tex]\( m = 20 \)[/tex]

So the correct answer is:
C. [tex]\( n = 10 ; u = 15 ; m = 20 \)[/tex]

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