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 t

Question

boyakko [2]

2 years ago

13

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 t

o buy 2 pens?

Mathematics

1 answer:

amm1812 · Answer 1 · 2023-07-05T09:04:14+03:00

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

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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.