Question

Aaron has a certain sum of money to buy stationery. He can buy x pens at $1.90 each and will
have 50 cents left. Alternatively, he can buy (x + 9) pencils at $0.70 each and have 20 cents
eft.
(a) Find the value of x.
(b) How much money does Aaron have to buy stationery?
(c) If Aaron buys 3 pens and uses the rest of the money to buy pencils, how many pencils
can he buy?

Answer 1

Answer:

(a) x = 5

(b) $10

(c) 6 pencils

Step-by-step explanation:

Part (a)

Let x = number of pens

Let (x + 9) = number of pencils

Let y = total sum of available money

Cost of pen = $1.90

Cost of pencil = $0.70

Create two equations from the given information

Equation 1:    1.9x = y - 0.5

Equation 2:   0.7(x + 9) = y - 0.2

Rewrite both equations to make y the subject:

Equation 1:    1.9x + 0.5 = y

Equation 2:   0.7(x + 9) + 0.2 = y

Equate the rewritten equations and solve for x:

1.9x + 0.5 = 0.7(x + 9) + 0.2

1.9x + 0.5 = 0.7x + 6.3 + 0.2

1.9x + 0.5 = 0.7x + 6.5

1.2x = 6

x = 5

Part (b)

Substitute x = 5 into one of the rewritten equations and solve for y:

1.9(5) + 0.5 = y

9.5 + 0.5 = y

y = 10

Therefore, Aaron has $10 to buy stationery

Part (c)

3 pens = 3 × $1.90 = $5.70

Therefore, $10 - $5.70 = $4.30

Cost of 1 pencil = $0.70

Number of pencils = $4.30 ÷ $0.70 = 6.1428...

Therefore, he can buy 6 pencils