Question

9 pens and five pencils cost $3.2 , and 7pens and 8 pencils cost $2.9. Find the unit price for each pen and pencil.

Answer 1

Let's say that pens=x and pencils=y

9x + 5y = 3.2

7x + 8y = 2.9

By multiplying the top by 7, we get

63x + 35y = 22.4

Move the 35y to the other side, we get

63x = 22.4 - 35y

By multiplying the bottom by 9, we get

63x + 72y = 26.1

By combining these, we get

(22.4 - 35y) + 72y = 26.1

Remove the parentheses and subtract the y's

22.4 + 37y = 26.1

Move the 22.4 to the other side

37y = 26.1 - 22.4 = 3.7

Divide both sides by 37

y = 3.7 / 37 = .1 or $0.10

Back to the original and substitute .1 for y

7x + 8(.1) = 2.9

7x + .8 = 2.9

7x = 2.9 - .8 = 2.1

Divide both sides by 7

x = 2.1 / 7 = .3 or $0.30

Pens = $0.30 and pencils cost $0.10

Answer 2

Answer:

x=0.3,y=0.1

Step-by-step explanation:

Elimination method

9x+5y=3.2 ........ eqn 1

7x+8y=2.9 ........ eqn 2

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Times eqn 1 by 8 and eqn 2 by 5 to balance the equations.

So the equations will turn into

72x+40y=25.6........ eqn 3

35x+40y=14.5........ eqn 4

Then there is common pronumerals so minus both eqn 3 and 4

This will equal

37x=11.1

x=0.3

Sub x=0.3 into eqn 2

7(0.3)+8y=2.9

2.1+8y=2.9

8y=0.8

y=0.1

x=0.3, y=0.1

∴ Pens cost $0.30 and Pencils cost $0.10