5-12
In 1955 an antique car that originally cost $3,668 is valued today at $62,125 if in excellent condition, which is 1¾ times as much as a car in very nice condition – if you can find an owner willing to part with one for any price, What would be the value of the car in very nice condition?
Let x = value of the car in very nice condition
1¾x = 62125
7x/4 = 62125 (multiply by 4)
7x = 248500 (divide by 7)
X = 35,500
$35000 = value of the car in very nice condition
5-14
Nanda Yueh and Lane Zuriff sell homes for ERA Realty. Over the past 6 months they sold 120 homes. Nanda sold 3 times as many homes as Lane. How many homes did each sell?
Let x = Number of homes sold by Lane
3x = Number of homes sold by Nanda
3x+x = 120
4x = 120 (divide by 4)
X = 30
30 = Number of homes sold by Lane
90 = Number of homes sold by Nanda
5-16
Dots sells 250 T-shirts ($2) and shorts ($4). In April, total sales were $600. How many T-shirts and shorts did Dots sell? Check your answer. Hint: Let S = Shorts
Let S = number of shorts sold
Let T = number of T-shirts sold
S + T = 250
4S + 2T = 600 (divide by 2)
2S + T = 300
T = 300 – 2S
S + (300 – 2S) = 250
S + 300 -2S = 250
-S = 250 – 300
-S = -50 (divide by -1)
S = 50
T = 300 – 2S
T = 300 – 2(50)
T = 300 – 100
T = 200 Check:
S + T = 250
50 + 200 = 250 (corrrect)
Therefore:
50 = number of shorts sold
200 = number of T-shirts sold
5-24
Jill, an employee at Old Navy, budgest 1/5 of her yearly salary for clothing. Jill’s total clothing bill for the year is $8000. What is her yearly salary?
Let x = yearly salary x/5 = 8000 (mutiply by 5)
1x = 40000
X = 40000
Jill’s yearly salary = $40000
5-26
The count of discouraged unemployed workers rose to 503000, 2½ times as many as in the previous year. How many discouraged unemployed workers were there in the previous year?
Let x = number discouraged of unemployed workers last year
2½x = 503000
5x/2= 503000 (multiply by 2)
5x = 1006000 (divide by 5)
X = 201200
201200 = Number of discouraged unemployed workers last year
5-28
Staples sells boxes of pens ($10) and rubber bands ($4). Leona ordered a total of 24 cartons for $210. How many boxes of each did Leona order? Check your answer. Hint: Let P = pens.
Let P = number of pens (boxes)
Let R = number of rubber bands (boxes)
P+R = 24
P = 24 – R
10P + 4R = 210 (substitute)
10( 24 – R ) + 4R = 210
240 – 10R + 4R = 210
240 – 6R = 210
-6R = 210 – 240
-6R = -30 (divide by -6)
R = 5
P = 24 – R
P = 24 – 5
P = 19
19 = number of boxes of pens Leona ordered
5 = number of boxes of rubber bands Leona ordered
5-34
At General electric, shift 1 produced 4 times as much as shift 2. General Electrics’ total production for July was 5500 jet engines. What was the output for each shift?
Let x = output of shift 2
Let 4x = output of shift 1
4X + x = 5500
5x = 5500 (divide by 5)
X = 1100
1100 jet engines= output of shift 2
4400 jet engines = output of shift 1
5-36
Jim Murray and Phyllis Lowe received a total of $50000 from a deceased relative’s estate. They decided to put $10000 in a trust for their nephew and divide the remainder. Phyllis received ¾ of the remainder; Jim received ¼. How much did Jim and Phyllis receive
Remainder = 50000 – 10000
Remainder = 40000
Let X = amount received by Jim
Let Y = amount received by Phyllis
X = ¼ (4000)
X = 10000
Y = ¾ (4000)
Y = 30000
Jim received $10000
Phyllis received $30000
5-38
Wal-Mart sells thermometers ($2) and hot-water bottles ($6). In December, Wal-Mart’s total sales were $1200. Customers bought 7 times as many thermometers as hot-water bottles. How many of each did Wal-Mart sell? Check your answer.
Let x = number of thermometers sold
Let Y = number of hot-water bottles sold
7Y = X
2x + 6y = 1200 (simplify)
X+3y=600 (substitute)
7y + 3y = 600
10y = 600 (divide by 10)
Y = 60
X= 7y
X= 7(60)
X = 420
420 = number of thermometers sold
60 = number of hot-water bottles sold
Check:
7y = x
7(60) = 420 (correct)
2x+6y = 1200
2(420) + 6(60) = 1200 (correct)
5-40
Kent Christy is organizing a fundraiser for the pool he manages. He bought ice-cream cones ($.75) and ice-cream sandwiches ($1.00) to sell. His total bill was $225. (a) If he ordered twice the number of ice-cream cones than ice-creamsandwiches, how many of each did he buy? (b) What did he spend for ice-cream cones? (c) What did he spend for ice-cream sandwiches?
(a)
Let x = number of ice-cream cones bought
Let y = number of ice-cream sandwiches bought
X = 2y
.75x + y = 225
.75(2y) = 225
1.5y + y = 225
2.5y = 225 (divide by 2.5)
Y = 90
X = 2y
X = 180
180 = number of ice-cream cones bought
90 = number of ice-cream sandwiches bought
(b)
180 x $.75
$135 = amount spent for ice-cream cones
(c)
90 x $1.00
$90 = amount spent for ice-cream sandwiches
