John and Smith went to a stationery shop.

Question

John bought 6 pens, 4 pencils and 3 erasers. Smith bought 3 pens, 8 pencils and 6 erasers and spent 20% more than John. What percentage money did John spend on pens?

How can I form an equation and solve?

Answer 1

Let the cost of John's 4 pencils and 3 erasers be x
then the cost of Smith's 8 pencils and 6 erasers is 2x , notice twice as many

cost of Smiths 3 pens --- y
cost of John's 6 pens ---- 2y , notice twice as many pens

Johns cost = 2y + x
Smith's cost = y + 2x

y + 2x = 1.2(2y + x)
y + 2x = 2.4y + 1.2x
.8x = 1.4y
8x = 14y
4x = 7y
y = 4x/7

percentage that john spent on pens
= 2y/(2y+x)
=(8x/7)/(8x/7 + x)
= (8x/7)/(15x/7)
= (8x/7)(7/15x
= 8/15
= appr 53.3%

check my arithmetic