Word Problems
Hot dogs sold= h Bags of popcorn sold = p
At a baseball game , the concession stand sold hotdogs and popcorn. Using the equation below, how many bags of popcorn were sold if there were 210 hot dogs sold? 6p-30=h
p= 40
6p-30=210
6p=240
p=40
Solve.
2x+2=10
x=4
2x=10-2
2x=8
x=4
Solve.
2x+5<9
x<2
2x<9-5
2x<4
x<4/2
x<2
Rewrite to solve for m:
y=mx+b
m=(y-b)/x
y-b=mx
y-b/x
How many solutions?
4x+2=4x+2
Infinite Solutions
x's cancel out, 2=2 is true
The material needed to repair a broken sink costs $341.25 and the total expected cost of the job is $424.09. The avg rate for a plumber in FL is $20.71/hr. How many hrs will the plumber be working?
4 hours
Solve.
x/4+2=18
x=64
x/4+2=18
x/4=18-2
x=16(4)
Solve.
4+6x < 10
x<1
6x<10-4
6x<6
x<1
Rewrite to solve for l
A=lwh
l=A/(wh)
How many solutions?
3x+7 = 2x- 7
One Solution
x's do not cancel out.
A software engineer charges a flat fee of $100 and an hourly price for his consulting services. A customer paid him $800 total, which included the flat fee and the hourly prices for 14 hours of his services. What is his hourly price?
$50 an hr
2x+15=x+29
x=14
2x+15=x+29
2x-x+15=29
x=29-15
x=14
Solve:
m/2-4>8
m>24
m/2 > 8+4
m/2>12
m>12(2)
m>24
Rewrite to solve for b
y= mx+b
b=y/(mx)
How many solutions?
2(x+4)+2x= 4x+6+2
Infinite Solutions
2(x+4)+2x=4x+6+2
2x+8+2x= 4x+8
4x+8=4x+8
x's cancel out. 8=8 is true
The dimensions of a rectangle are 7 inches by 2.5x inches. The perimeter of the rectangle is less than 31 inches. What is the largest value of x?
3
2-3b=-b
b=1
2=-b+3b
2=2b
1=b
Solve this inequality.
150 is always less than 65 plus a number x
x<85
65+x<150
x<150-65
x< 85
Rewrite to solve for b2
a2+b2=c2
b2=c2-a2
How many solutions?
3x+6=3x-6
No Solutions
x's cancel out. 6=-6 is false.
The max weight a truck can safely carry is 30,000 lbs. A driver is moving boxes into the truck. Each box contains 6 of the same types of tables, and each table weighs 90 lbs. The driver weighs 200 lbs.
What is the maximum number of boxes the driver can move into the truck?
55 boxes
Solve.
2/9x-4=10
x=63
2/9x-4=10
2/9x=14
x=63
Solve.
18+8x<4x-6+3x+31
x<7
18+8x<7x+25
8x-7x<25-18
x<7
Rewrite to solve for h.
A=1/2bh
h=(2A)/b
How many solutions?
2(3x+2x)+4x-2x+5-3=6(2x+1)-8
No Solutions
2(3x+2x)+4x-2x+5-3=6(2x+1)-8
6x+4x+2x+2=12x+6-8
12x+2=12x-2
x's cancel out . 2=-2 is false.