Gabby bought 4 pens and 5 pencils for $6.71. Sydney bought 5 pens and 3 pencils for $7.12. Find the cost of each.

Question

Gabby and Sydney bought some pens and pencils. Gabby bought 4 pens and 5 pencils for $6.71. Sydney bought 5 pens and 3 pencils for $7.12. Find the cost pf each.

Answer 1

With most word problems, what you need to do is to set up the right equations:

 

First let X=pens and Y=pencils.

 

4x + 5y = 6.71  4 pens + 5 pencils = 6.71

5x + 3y = 7.12   5 pens + 3 pencils = 7.12

______________

 

Now solve for x or for y.  I choose to solve for y.  So I multiply the top equation by 5 and the bottom equation by 4.

20x + 25y = 33.55

20x + 12y = 28.48

________________

 

Subtracting the bottom equation from the top:

13y = 5.07

y = .39  The pencils are .39 each

 

How much are the pens?

Use either of the two equations I first wrote down:

4x + 5y = 6.71

4x + 5(.39) = 6.71

4x + 1.95 = 6.71

4x = 4.76

x = 1.19  the pens costs 1.19 each

Answer 2

pen (p) and pencil (c). 2 equations in 2 unknowns 

equation 1

4p + 5c = 6.71

equation 2

5p +3c = 7.12

 

from eq2, c = (7.12-5p)/3 

substitute in eq1, you get

4p + 11.867 - 8.33p = 6.71

p = $1.19

c= (7.12 - 5 x 1.19)/3

c= $0.39

 

the price of a pen is $1.19

the price of a pencil is $0.39

 

check: substitute in eq1 and you will get $6.71