Solving a Two-Step Equation
How do you solve a two-step equation?
You use inverse operations to isolate the variable. / You use PEMDAS backwards (SADMEP).
Write the equation: The sum of three times a number d and 5 is 17.
3d + 5 = 17
2(5k-3)=44
k=5
-(3s-5)=-13
s=6
Solve for x:
0.5 (4x - 6)=11
x=7
8a + 25 = 89
a = 8
As a membership fee, a health club charges a one-time amount of $40 and charges $25 for each month. The total fee after m months is $240. Write the equation that represents this situation.
40 + 25m = 240
6(3x-5)-8x=47
x=7.7
-5(4w+8) = 100
w=-7
Solve for w:
3/5 (w-5) = 24
w=45
c/7 - 31 = -29
c = 14
A customer’s total cell phone bill this month is $50.50. The company charges a monthly fee of $18 plus five cents for each call. Use n to represent the number of calls.
50.50 = 18 + 0.05n or 0.05n + 18 = 50.50
Write the equation: A family buys 4 airline tickets online. The family buys travel insurance that costs $22 per ticket. The total cost is $1,546. Let t represent the price of one ticket. Write an equation for the total cost.
4(t+22)=1546
-2(5+6m) +16 = -126
m=11
Solve for c:
1/3 (9c - 36) = -9
c=1
-7x+30=58
x = -4
A taxi charges $1.75 plus a fee of $0.75 for each mile traveled. The total cost of a ride, without a tip, is $4.75. How many miles is the trip? Use m for the number of miles traveled. Write and solve the equation.
1.75 + 0.75m = 4.75
m = 4 miles
Write the equation and solve: A family buys 8 train tickets, t. Each ticket has an added cost of $12.75 for a lunch. The total cost is $342. Let t represent the price of one ticket. Write an equation for the total cost. Then find the price of one ticket.
8(t+12.75) = 342
t=$30
22 -5(6v-1) = -93
v=4
Write and solve:
AMD seventh graders received ⅓ of the total funds raised from cookies and brownies at the bake sale. The funds raised for selling cookies were $84. The seventh graders received a total of of $60. What were the funds raised for the brownies, b?
1/3 (84 + b)=60
b = $96
3.6=1.5−0.7z
z = -3
Chloe paid $65 for vans and then bought 5 pairs of equally priced socks. She spent a total of $104.95. If s represents the price of one pair of socks, write the equation that represents this situation AND solve for s, to find the price of one pair of socks.
65 + 5s = 104.95 or 5s + 65 = 104.95
s= $7.99
In December, seven friends went ice skating at Rockefeller Center and spent $25 per ticket. They also each rented a pair of skates, s. The friends spend a total of $245. Let s represent the price of the skate rental. Write and solve the equation.
7 (s+25)=245
s=$10
-2(3x+15) - (9+6x) = 105
x = -12
Write and solve:
Bailey has d dollars. He spends $76.30 on new sneakers. He decides to keep 1/2 of what he has left, which is $16.31. How many dollars did Bailey have originally?
1/2 (d-76.30)=16.31
d=$108.92