2007 AMC 10A Problem 5

Attempt Problem 5 of the 2007 AMC 10A below, then check your answer against the professionally curated solution from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2007 AMC 10A solutions, or check the answer key.

All problems are used with official legal permission of the Mathematical Association of America (MAA).

5.

A school store sells

7

pencils and

8

notebooks for

\$4.15.

It also sells

5

pencils and

3

notebooks for

\$1.77.

How much do

16

pencils and

10

notebooks cost?

\$4.76

\$5.84

\$6.00

\$6.16

\$6.32

Answer: B

Concepts:system of equations money

Difficulty rating: 1020

Small hint:

Work in cents: let

p

be a pencil and

n

a notebook, giving

7p + 8n = 415

and

5p + 3n = 177

Big hint:

Solve for

p

and

n,

then evaluate

16p + 10n

Solution:

Let

p

and

n

be the prices in cents of a pencil and a notebook. Then

7p + 8n = 415

5p + 3n = 177.

Solving this system gives

p = 9

and

n = 44.

So

16

pencils and

10

notebooks cost

16(9) + 10(44) = 584

cents, or

\$5.84.

Thus, the correct answer is B.