Section 3.2 – Problem Solving
Number Problems
Numbers The sum of two numbers is 25. The
difference of two numbers is 3. Find the
numbers.
x  first number  14
y  second number  11
 x  y  25

x  y  3
2 x  28
x  14
14  y  25
y  11
Use Elimination
Number Problems
Numbers Juan is thinking of two numbers. He says that 3
times the first number minus the second number is 118. In
addition, two times the first number plus the second number is
147. Find the numbers.
x  first
first number
number  53
y  second number
number  41
 3 x  y  118

 2 x  y  147
5 x  265
x  53
3 ( 53 )  y  118
159  y  118
41  y
Use Elimination
Revenue and Cost
Revenue Let R ( x )  16 x represent a
company’s revenue, let C ( x )  7 x  3645
represent the company’s cost, and let x
represent the number of units produced and
sold each day. Find the company’s break-even
point; that is, find x so that R = C.
 R ( x )  16 x

 C ( x )  7 x  3645
Use Substitution
R(x)  C (x)
16 x  7 x  3645
9 x  3645
x  405 units
Perimeter
Perimeter The perimeter of a rectangle is 260 centimeters. If
the width of the rectangle is 15 centimeters less than the length,
what are the dimensions of the rectangle?
2 x  2 ( x  15 )  260
x  length  72.5 cm
y  width  57.5 cm
 x  x  y  y  260

 y  x  15
 2 x  2 y  260

 y  x  15
Use Substitution
2 x  2 x  30  260
4 x  30  260
4 x  290
x  72 . 5
y  72 . 5  15
y  57 . 5
Mixtures
Investments Marge and Homer have $80,000 to invest. Their
financial advisor has recommended that they diversify by placing
some of the money in stocks and some in bonds. Based upon
current market conditions, he has recommended that three times
the amount in bonds should equal two times the amount invested
in stocks. How much should be invested in stocks? How much
should be invested in bonds?
x  amount invested in stocks  $ 48 , 000
3 y  2 ( 80000  y )
y  amount invested in bonds  $ 32 , 000
3 y  160000  2 y
5 y  160000
 x  y  80000

3 y  2 x
3 y  2 ( 80000  y )
Use Substitution
y  160000
x  80000  y
3 y  160000  2 y
y  32000
x  32000  80000
x  48000
Mixtures
Candy A candy store sells chocolate-covered almonds for $6.50 per pound
and chocolate-covered peanuts for $4.00 per pound. The manager decides to
make a bridge mix that combines the almonds with the peanuts. She wants
the bridge mix to sell for $6.00 per pound, and there should be no loss in
revenue from selling the bridge mix versus the almonds and peanuts alone.
How many pounds of chocolate-covered almonds and chocolate-covered
peanuts are required to create 50 pounds of bridge mix?
x  # pounds almonds  40 lbs
x  50  y
y  # pounds peanuts  10 lbs
6 . 50 ( 50  y )  4 y  300
 x  y  50

 6 . 50 x  4 . 00 y  6 . 00 ( 50 )
325  6 . 50 y  4 y  300
 x  y  50

 6 . 50 x  4 y  300
 2 . 50 y   25
Use Substitution
325  2 . 50 y  300
y  10
x  10  50
x  40