SOLUTION: I am currently taking Algebra 1, and need assistance with the following word problems (that use substitution, of course): 1.)Lisa and Beverly had just $5 to spend for an after-s

Question 183621: I am currently taking Algebra 1, and need assistance with the following word problems (that use substitution, of course):
1.)Lisa and Beverly had just $5 to spend for an after-school snack. They could have bought 2 hamburgers and 1 carton of milk with no change back or 1 hamburger and 2 cartons of milk with 40 cents change back. How much does a carton of milk cost?
2.)If you buy six pens and one mechanical pencil, you'll get only $1 change from your $10 bill. But if you buy four pens and two mechanical pencils, you'll get $2 change. How much does each pen and each pencil cost?
3.)One number is 16 more than another. If the smaller number is subtracted from two-thirds of the larger number, the result is one-fourth of the sum of the two numbers. Find the numbers.

Thank you very much! An answer as immediate as possible would be greatly appreciated.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1.)Lisa and Beverly had just $5 to spend for an after-school snack. They could have bought 2 hamburgers and 1 carton of milk with no change back or 1 hamburger and 2 cartons of milk with 40 cents change back. How much does a carton of milk cost
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2h + c = 500 cents
h + 2c= 460 cents
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Prepare for substitution:
c = 500 -2h
-----------------------
Substitute to solve for "h":
h + 2(500-2h) = 460
h 1000 -4h = 460
-3h = -540
h = 180 cents = $1.80 (the price of a hamburger)
-----------------
Substitute to solve for "c":
c = 500 - 2(180)
c = 500 - 360
c = 140 cents = $1.40 (the price of a carton of mild)
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2.)If you buy six pens and one mechanical pencil, you'll get only $1 change from your $10 bill. But if you buy four pens and two mechanical pencils, you'll get $2 change. How much does each pen and each pencil cost?
---
Equations:
6p + m = 900 cents
4p +2m = 800 cents
------------------
Prepare for substitution:
m = 900-6p
--------------
Substitute to solve for "p":
4p + 2(900-6p) = 800
4p + 1800 - 12p = 800
-8p = -1000
p = 125 cents = $1.25 (price of a pen)
----------
Substitute to solve for mechanical pencil:
m = 900 - 6p
m = 900 - 6(125)
m = 900 - 750 = 150 cents = $1.50 (price of a mechanical pencil)
----------------------------------------------------

3.)One number is 16 more than another. If the smaller number is subtracted from two-thirds of the larger number, the result is one-fourth of the sum of the two numbers. Find the numbers.
---
Equations:
x = y - 16
(2/3)y - x = (1/4)(x+y)
---------------
Simplify the 2nd equation:
8y - 12x = 3x + 3y
15x = 5y
x = (1/3)y
-------------------
Substitute to solve for "Y":
(1/3)y = y - 16
(2/3)y = 16
(1/3)y = 8
y = 24
-------------
Substitute to solve for "x":
x = (1/3)y = 8
=============================
Cheers,
Stan H.

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