four pencils and a ruler cost $1. six pencils and three rulers cost $2.10. find the cost of three pencils and thirteen rulers.

$ 5.65

Step-by-step explanation:

let the cost of a pencil and a ruler be $p and $r respectively.

4p +r= 1 (1)

6p +3r= 2.10

divide by 3 throughout:

2p +r= 0.70 (2)

Q: 3p +13r= ?

(1) -(2):

(4p +r) -(2p +r)= 1 -0.70

4p +r -2p -r= 0.30 (expand)

2p= 0.30 (simplify)

p= 0.30 ÷2 (÷2 on both sides)

p= 0.15

subst. into (1):

4(0.15) +r= 1

r +0.60= 1

r= 1 -0.60

r= 0.40

cost of three pencils and thirteen rulers

= 3p + 13r

= 3(0.15) + 13(0.40)

= 0.45 + 5.20

= $5.65