Write Equations and Inequalities
Riley has $60 and saves $7 per week. John, her brother, has $120 and saves $5 per week. Write an equation that represents the number of weeks it will take for Riley and John to save the same amount of money.
7x + 60 = 5x + 120
3x + 5 = 12
(Solution in fraction form)
x= 7/3
2x + 3 = x + 9
x = 6
(x/4) + 5 = x + 4
x= 4/3
The perimeter of an equilateral triangle is 90 inches. If one of the sides is equal to 3x, what is the value of x?
x= 10
James has $1,200 and spends $50 per week. Alex has $400 and saves $50 per week. Write an equation that represent the number of weeks it will take for James and Alex to save the same amount of money.
-50x + 1200 = 50x + 400
5x + 6 = -14
x= -4
1.5x + 2 = .5x + 10
x= 8
(x/5) + 6 = (3x/5) + 10
x= -10
Richard’s Rental Car charges a $55 rental fee and $0.25 per mile. Fidel’s Rental Car charges a $45 rental fee and $0.35 per mile. At how many miles is the cost the same for both companies?
x= 100
Sierra has a bucket that originally contained 340 fl oz water and is being filled at a rate of 5 fl oz per minute. Brian has a bucket that originally contained 650 fl. oz. of water and is being drained at a rate of 8 fl oz per minute. What is the number of minutes that need to pass in order for the two buckets to contain the same amount of water?
5x + 340 = -8x + 650
x/5 - 2 = 5
x= 35
0.6x - 5 = 0.1x + 7
x= 24
3x + 2/7 = 2x + 5/7
x= 3/7
A square with a side length of 2x has the same perimeter as a rectangle with a length of 3x and width of 3. What is the value of x?
x= 3
Veronica is ordering trophies for her school. Company P charges $3.50 for each trophy and a one-time engraving fee of $25. Company R charges $7.50 for each trophy and a one-time engraving fee of $17. Which inequality can be used to find the minimum number of trophies that can be ordered so that the total charge at company P is less than the charge at Company R?
3.5x + 25 < 7.5x + 17
-3x - 13 = -25
x= 4
12x - 15 = -3x + 6
x= 1.4
(3x/5) + 3/2 = (4x/5) + 9/2
x= -15
Aquarium I contains 4.6 gallons of water. Louise will begin filling Aquarium I at a rate of 1.2 gallons per minute. Aquarium II contains 54.6 gallons of water. Isaac will begin draining Aquarium II at a rate of 0.8 gallons per minute. After how many minutes will both aquariums contain the same amount of water?
x= 25 mins.
Helen had $330 in her savings account when Vince opened a savings account with $0.
Which inequality represents the situation when the amount of Helen’s account was greater than the amount of money in Vince’s account?
50x < 330 + 30x
(1/4)x + 2 = 3/4
x= -5
1.75x-.25=-0.50x+2.25
(Solution in decimal form)
x= 1.1111
(-x/4) + 3/8 = (x/2) - 3/4
x= 3/2
A rectangle's perimeter and its area have the same numerical value. The width of the rectangle is 3 units. What is the length of the rectangle in units?
L= 6