Two-Step Equations
2x + 4 = 10
x = 3
Is x = 4 the correct solution to the equation 3x = 12?
Yes. (3 times 4 = 12)
Sarah has some apples. She buys 4 more and now has 12. Write an equation using a for the starting number of apples.
a + 4 = 12
2(x + 3) = 10
x = 2
A gym membership costs $10 a month plus a one-time $20 sign-up fee. If Sarah paid $50 in total, write an equation and solve to find how many months (m) she paid for.
Equation: 10m + 20 = 50
Solution: m = 3 months.
3y - 2 = 13
y = 5
Is y = 5 the correct solution to the equation y + 7 = 11?
No. (5 + 7 = 12, not 11)
A box of cookies is shared equally among 3 friends. Each gets 5 cookies. Write an equation using c for the total cookies.
c / 3 = 5
(y + 4) / 2 = 5
y = 6
A farmer packages apples into baskets. He has 3 full baskets and 4 loose apples left over, making a total of 25 apples. Write an equation and solve to find how many apples (a) are in each basket.
Equation: 3a + 4 = 25
Solution: a = 7 apples.
4a + 5 = 21
a = 4
Is m = 10 the correct solution to the equation m / 2 = 5?
Yes. (10 / 2 = 5)
Tom earns $8 an hour. He made $32. Write an equation using h for the number of hours he worked.
8h = 32
3(m - 1) = 12
m = 5
You buy 4 identical notebooks and one fancy pen that costs $3. Your total cost is $19. Write an equation and solve to find out how much each notebook (n) costs.
Equation: 4n + 3 = 19
Solution: n = 4 dollars.
5m - 5 = 20
m = 5
Is k = 3 the correct solution to the equation 4k - 2 = 10?
Yes. (4 times 3 - 2 = 10)
Emily had 20 stickers. She gave some away and has 8 left. Write an equation using s for the stickers she gave away.
20 - s = 8
(p - 2) / 3 = 4
p = 14
The 5th-grade class is raising money. They had $15 in their cash box already. They sold 5 tickets to the school play, and now they have $40 total. Write an equation and solve to find the cost of each ticket (t).
Equation: 5t + 15 = 40
Solution: t = 5 dollars.
2p + 8 = 20
p = 6
Is p = 6 the correct solution to the equation 2p + 3 = 12?
No. (2 times 6 + 3 = 15, not 12)
A plant grows 2 cm every week. It grew a total of 14 cm. Write an equation using w for the number of weeks.
2w = 14
4(k + 2) = 24
k = 4
A fish tank starts with 50 liters of water. Water drains out at a rate of 5 liters per minute. There are 20 liters left in the tank. Write an equation and solve to find how many minutes (m) the water has been draining.
Equation: 50 - 5m = 20
Solution: m = 6 minutes.