Question 86509
1.A collection of 30 coins worth $5.50 consists of nickels, dimes, and quarters. There are twice as many dimes as nickels. How many quarters are there?
:
The number of each coin equation:
n + d + q = 30
:
The $ amt equation:
.05n + .10d + .25q = 5.50
:
"There are twice as many dimes as nickels" equation:
d = 2n
:
Substitute 2n for d in both equations
n + 2n + q = 30
and
.05n + .10(2n) + .25q = 5.50
Which is:
3n + q = 30
and
.25n + .25q = 5.50
:
Multiply the above equation by 4 and subtract it from  3n + q = 30
3n + 1q = 30
1n + 1q = 22
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2n + 0q = 8
n = 8/2
n = 4 nickels
:
Then we know that d = 2(4) = 8 dimes
:
Use the coins equation to find q:
4 + 8 + q = 30
q = 30 - 12
q = 18 quarters
:
Check solutions using the $ equation:
.05(4) + .10(8) + .25(18) = 
.20 + .80 + 4.50 = 5.50
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2.the school cafeteria sells milk at 25 cents per carton and salads at 45 cents each. One week the total sales for these items were $1,322.50. How many salads were sold that week?
:
Seems like more information is needed for this one, the way it is:
It could be 1000 salads and 3490 milks
or 2000 salads and 1690 milks
or 3000 salads and 110 milks
:
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3.At the homecoming football game, Senior Class Officers sold slices of pizza for $.75 each and hamburgers for $1.35 each. They sold 40 more slices of pizza than hamburgers, and sales totaled $292.50. How many slices of pizza did they sell?
:
Let x = no. of slices of pizza sold
Then
(x-40) = no. of hamburgers sold
:
.75x + 1.35(x-40) = 292.5
.75x + 1.35x - 54 = 292.5
2.10x = 292.5 + 54
2.10x = 346.5
x = 346.5/2.1
x = 165 slices of pizza
:
Check solution; 165-40 = 125 hamburgers
.75(165) + 1.35(125) = 
123.75 + 168.75 = 292.50
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4.For a recent job, a plumber earned $28/hour, and the plumber's apprentice earned $15/hour. The plumber worked 3 hours more than the apprentice. If together they were paid $213, how much did each earn? (Hint: First write an expression for the number of hours each worked on the job?
:
Let x = apprentice hrs
Then
(x+3) = plumber's hrs
:
15x + 28(x+3) = 213
15x + 28x + 84 = 213
43x = 213 - 84
x = 129/43
x = 3 hrs worked by the apprentice
3 + 3 = 6 hrs worked by the plumber
:
Check solution:
6(28) + 3(15) =
168 + 45 = 213
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5.A plane whose air speed is 150 miles per hour flew from Abbot to Blair in 2 hours with a tail wind. On the return trip against the same wind, the plane was still 60 miles from Abbot after 2 hours. Find the wind speed and the distance between Abbot and Blair.
:
Let x = wind speed
Let y = one-way distance
:
With the wind equation: 2(150+x) = y
Against the wind equation: 2(150-x) + 60 = y
:
Rearrange the two equations to:
+2x - y = -300
-2x - y = -360
--------------   add
0x - 2y = -660
y = -660/-2
y = 330 mi is the distance
:
Find x:
2x - y = -300
2x - 330 = -300
2x = 330 - 300
x = 30/2
x = 15 mph is the wind
:
Check solutions: 
2(150+15) =
2 * 165 = 330
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6.The cost of an adult ticket to a football game is $1.75. The cost of a student ticket is $1.25. Total receipts last week from ticket sales were $1,700. If the number of students tickets sold was twice the number of adult tickets, how many of each type were sold
:
Let x = no. of adult tickets
Then
2x = no. of student tickets
:
1.75x + 1.25(2x) = 1700
1.75x + 2.50x = 1700
4.25x = 1700
x = 1700/4.25
x = 400 adults, then 800 students
:
Check solutions:
1.75(400) + 1.25(800)
 700 + 1000 = 1700