Creating Linear Equations
A meteorologist is monitoring a rain gauge. The gauge started with 3 inches of rain in it. Then it started raining 2 inches per hour. How many hours did it rain if there are 17 inches in the rain gauge?
Write an equation that represents this situation.
2x+3=17
OR
3+2x=17
24-5d=d
d=4
Solve the following for F:
5(F-2)=C
F=C/5+2
Amanda rented a bike from Shawna's Bikes. They charged her $2 per hour, plus a $10 fee. Amanda paid less than $27.
Write an inequality that represents this situation.
2x+10<27
5x+3>18
x>3
A cable guy charges $75 for a house call. He also charges $30 an hour. If Mrs. Lugo’s bill is $315, how many hours did the cable guy work?
Write an equation that represents this situation.
30x+75=315
OR
75+30x=315
(6x+3)/3=-7
x=-4
Solve the following for x:
4x+2y=z
x=(z-2y)/4
OR
x=(z-y)/2
Bill spent less than $26 on a magazine and five composition books. The magazine cost $4.
Write an inequality that represents this situation.
5x+4<26
4(x-2)>-16
x>-2
The second of two numbers is 9 more than 4 times the first. Their sum is 44.
Write an equation that represents this situation.
4n+9+n=44
OR
5n+9=44
3x+19=9x-11
x=5
Solve for y:
xy-d=m
y=(m+d)/x
More than 450 students went on a field trip. Ten buses were filled and 5 more students traveled in a car.
Write an inequality that represents this situation.
10x+5>450
-2x+9≤25
x≥-8
The length of a rectangle is one more than five times the width. If the perimeter is 146 feet, find the width.
Write an equation that represents this situation.
5w+1+5w+1+w+w=146
OR
12w+2=146
4x-2=10+2x
x=6
Solve for w:
p=2l+2w
(p-2l)/2=w
OR
p/2-l=w
Nicholas wants to order a pizza. He has a total of $13.00. The pizza costs $7.50 plus $1.25 per topping. How many toppings can Nicholas order?
Write an inequality that represents this situation.
1.25t+7.50≤13.00
-6x-17≥8x+25
x≤-3
Two trains left Mooseport at the same time. One traveled north at 95 mph. The other traveled south at 87 mph. After how many hours were the two trains 1092 miles apart?
Write an equation that represents this situation.
95h+87h=1092
OR
182h=1092
12x-5=-6x+13
x=1
Solve for x:
y=mx+b
(y-b)/m=x
Elisa won 40 lollipops playing basketball at the school fair. She gave two to every student in her math class. She has at least 7 lollipops left.
Write an inequality that represents this situation.
40-2x≥7
-21(x+33)<84
x>-37