Chapter 8 Systems of Equations and Inequalities

55. Let l be the length of the rectangle and w be
the width of the rectangle. Then:
l = 2w
and 2l+ 2w= 90
Solve by substitution:
2(2 w) + 2w= 90
4w+ 2w= 90
6w= 90
w = 15 feet
l = 2(15) = 30 feet
The floor is 15 feet by 30 feet.
56. Let l be the length of the rectangle and w be
the width of the rectangle. Then:
l = w+
50 and 2l+ 2w= 3000
Solve by substitution:
2( w+ 50) + 2w= 3000
2w+ 100 + 2w= 3000
4w = 2900
w = 725 meters
l = 725 + 50 = 775 meters
The dimensions of the field are 775 meters by
725 meters.
57. Let x = the number of commercial launches and
y = the number of noncommercial launches.
Then: x+ y = 55 and y = 2x+ 1
Solve by substitution:
x+ (2x+ 1) = 55 y = 2(18) + 1
3x= 54 y = 36 + 1
x = 18 y = 37
In 2005 there were 18 commercial launches and 37
noncommercial launches.
58. Let x = the number of adult tickets sold and y
= the number of senior tickets sold. Then:
⎧ x+ y = 325
⎨
⎩9x+
7 y = 2495
Solve the first equation for y: y = 325 − x
Solve by substitution:
9x+ 7(325 − x)
= 2495
9x+ 2275 − 7x = 2495
2x = 220
x = 110
y = 325 − 110 = 215
There were 110 adult tickets sold and 215 senior
citizen tickets sold.
Section 8.1: Systems of Linear Equations: Substitution and Elimination
785
59. Let x = the number of pounds of cashews.
Let y = is the number of pounds in the mixture.
The value of the cashews is 5x .
The value of the peanuts is 1.50(30) = 45.
The value of the mixture is 3y .
Then x + 30 = y represents the amount of mixture.
5x+ 45= 3yrepresents
the value of the mixture.
Solve by substitution:
5x+ 45= 3( x+
30)
2x= 45
x = 22.5
So, 22.5 pounds of cashews should be used in
the mixture.
60. Let x = the amount invested in AA bonds.
Let y = the amount invested in the Bank
Certificate.
a. Then x+ y = 150,000 represents the total
investment.
0.10x+ 0.05y = 12,000 represents the
earnings on the investment.
Solve by substitution:
0.10(150,000 − y) + 0.05y = 12,000
15,000 − 0.10y+ 0.05y = 12,000
− 0.05y =−3000
y = 60,000
x = 150,000 − 60,000 = 90,000
Thus, $90,000 should be invested in AA
Bonds and $60,000 in a Bank Certificate.
b. Then x+ y = 150,000 represents the total
investment.
0.10x+ 0.05y = 14,000 represents the
earnings on the investment.
Solve by substitution:
0.10(150,000 − y) + 0.05y = 14,000
15,000 − 0.10y+ 0.05y = 14,000
− 0.05y =−1000
y = 20,000
x = 150,000 − 20,000 = 130,000
Thus, $130,000 should be invested in AA
Bonds and $20,000 in a Bank Certificate.
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