problems about numbers
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Problems about NumbersIf one more than three times a number is divided by the number, the result is four thirds. Find the number.
3x
3 3 1x xx
3 3 1 4x x
9 3 4x x
5 3x 35
x
LCD = 3x1x
43
3
3 4x
9 4 3x x
5.6 – Applications
Problems about Work Mike and Ryan work at a recycling plant. Ryan can sort a batch of recyclables in 2 hours and Mike can sort a batch in 3 hours. If they work together, how fast can they sort one batch?
Time to sort one batch (hours)
Fraction of the job completed in one hour
Ryan
Mike
Together
12131x
2
3
x
5.6 – Applications
Problems about Work Time to sort
one batch (hours)
Fraction of the job completed in one hour
Ryan
Mike
Together
12131x
2
3
x
12 6 1
2x
3x 5 6x 65
x hrs.
LCD =13
1x
6x 3
6 1x 16x
x
2x 6115
5.6 – Applications
James and Andy mow lawns. It takes James 2 hours to mow an acre while it takes Andy 8 hours. How long will it take them to mow one acre if they work together?
Time to mow one acre (hours)
Fraction of the job completed in one hour
James
Andy
Together
2
8
x
12181x
5.6 – Applications
Time to mow one acre (hours)
Fraction of the job completed in one hour
James
Andy
Together
2
8
x
12181x
LCD:12
8 12
x
4x 5 8x 85
x
hrs.
18
1x
8x 8
8 1x 18x
x
x 8315
5.6 – Applications
A sump pump can pump water out of a basement in twelve hours. If a second pump is added, the job would only take six and two-thirds hours. How long would it take the second pump to do the job alone?
112
1x
263
1203
Time to pump one basement (hours)
Fraction of the job completed in one hour
1st pump
2nd pump
Together
x
12
203
5.6 – Applications
112
1x
263
1203
Time to pump one basement (hours)
Fraction of the job completed in one hour
1st pump
2nd pump
Together
x
12
112
1 112 x
203
1x
1203
320
5.6 – Applications
LCD:
60 112
x
5x
60 4xhrs. 15x
1 1 312 20x
60x
160x
x 0
60 32
x
60 9x
5x60 9x
5.6 – Applications
Distance, Rate and Time Problems If you drive at a constant speed of 65 miles per hour and you travel for 2 hours, how far did you drive?
d r t
65mileshour
2 hours 130 miles
d tr
d rt
5.6 – Applications
A car travels six hundred miles in the same time a motorcycle travels four hundred and fifty miles. If the car’s speed is fifteen miles per hour faster than the motorcycle’s, find the speed of both vehicles.
Rate Time Distance
Motor-cycle
Car
x
x + 15
450 mi
600 mi
t
t
rdt
x450
15600x
5.6 – Applications
Rate Time Distance
Motor-cycle
Car
x
x + 15
450 mi
600 mi
t
t
rdt
x450
15600x
x450
15
600x
LCD: x(x + 15)
15600450
xx
x(x + 15) x(x + 15)
5.6 – Applications
15600450
xx
x(x + 15) x(x + 15)
xx 60045015
xx 60015450450
x15015450
x
15015450
x45
45x mphMotorcycle
6015 x mphCar
5.6 – Applications
Rate Time Distance
UpStream
DownStream
A boat can travel twenty-two miles upstream in the same amount of time it can travel forty-two miles downstream. The speed of the current is five miles per hour. What is the speed of the boat in still water? boat speed = x
x - 5
x + 5
22 mi
42 mi
t
t
rdt
522x
542x
5.6 – Applications
Rate Time Distance
UpStream
DownStream
boat speed = x
x - 5
x + 5
22 mi
42 mi
t
t
rdt
522x
542x
522x
5
42x
LCD: (x – 5)(x + 5)
542
522
xx(x – 5)(x + 5) (x – 5)(x + 5)
5.6 – Applications
542225 xx
2104211022 xx
xx 2242210110
x20
320
x1616 mph
Boat Speed
542
522
xx(x – 5)(x + 5) (x – 5)(x + 5)
x20320
5.6 – Applications
2855
Review of Long Division
783 4
4 7835 2855
2535
7
350
438362
19
3
5
203
5.7 – Division of Polynomials
43195
43195
72812 2 xxxx4
xx 48 2 x6 7
3
36 x
4
12 x
12434x
x 728 2 xx
124
x
Long Division
12728 2
xxx
5.7 – Division of Polynomials
35125 2 xxxx
xx 52 x7 35
7
357 x
0
5x 7x 35122 xx
Long Division
535122
xxx
5.7 – Division of Polynomials
15023 2 xxxx2
xx 62 2 x6 15
6
186 x
3
3x
3362x
x 152 2 x
33
x
Long Division
3152 2
xx
5.7 – Division of Polynomials
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