The sum of two books and a pencil is $6.00. The difference of cost between 3 books and 2 pencils is $ 2.00. Find the cost of a b
1 answer:
Answer:
The book costs $2 and the pencil also costs $2.
Step-by-step explanation:
It is easy to get the value of the book and the pencil if we use<em> algebraic expressions.</em>
Let x be the cost of the book and let y be the cost of the pencil.
The sum of 2 books and a pencil is $6.00
- 2x + y = $6.00
The difference of cost between 3 books and 2 pencils is $2.00.
- 3x - 2y = $2.00
Step 1: Let's get the value of y first.
2x + y = 6
y = 6 - 2x
Step 2: Let's substitute the value of y and look for the value of x.
3x - 2y = $2.00
3x - 2(6-2x) = 2
3x - 12 + 4x = 2
7x = 12 + 2
7x = 14
x =
x = $2 (this is the cost of the book)
Step 3: Let's substitute the value of x and look for the value of y.
2x + y = 6
2 (2) + y = 6
4 + y = 6
y = 6 - 4
y = $2 (this is the cost of the pencil)
Let's check:
2x + y = $6
2(2) + 2 = 6
4 + 2 = 6
6 = 6<em> (CORRECT)</em>
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