76,617 views
26 votes
26 votes
Daniel has $100. After he buys 4 pencils and 3 pens, he has $7 left. If each pencil costs $3 more than each pen, is $25 enough to buy 2 pens?

User Prashant Tapase
by
2.5k points

1 Answer

26 votes
26 votes

Answer: Yes, Daniel has enough money to buy 2 pens.

=========================================================

Step-by-step explanation:

x = cost of one pencil

y = cost of one pen

4x = cost of 4 pencils

3y = cost of 3 pens

4x+3y = cost of 4 pencils and 3 pens

100 - (4x+3y) = amount Daniel has left = 7 dollars

100-(4x+3y) = 7 is one equation we can form

Another equation we can form is x = y+3 because "each pencil costs $3 more than each pen".

Let's plug that into the first equation and solve for y.

100-(4x+3y) = 7

100-(4(y+3)+3y) = 7

100 - (4y+12+3y) = 7

100 - (7y+12) = 7

100 - 7y - 12 = 7

-7y + 88 = 7

-7y = 7-88

-7y = -81

y = -81/(-7)

y = 11.57 is the cost of one pen

2y = 2*11.57 = 23.14 is the cost of two pens.

Since this is less than $25, this means he has enough to buy two pens. This assumes that we either ignore tax, or the tax is already included in the listed prices.

User Yogie
by
2.9k points