Two-Step Equations - Integers: Score: Name | PDF | Mathematics - Free Printable

Let's solve each problem step by step using two-step equations with integers.

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1) Dalia bought a few swirl marbles and divided it equally among four of her friends and her brother, Jake. While playing, Jake lost 2 marbles and has only 7 marbles at present. Find how many marbles did Dalia buy in all.

#### Step-by-step:
- Jake now has 7 marbles, but he lost 2, so before losing, he had:
$ 7 + 2 = 9 $ marbles.
- Since the marbles were divided equally among 4 friends + Jake = 5 people, each person got 9 marbles.
- So total marbles Dalia bought:
$ 5 \times 9 = 45 $

✔ Answer: 45 marbles

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2) A bus departed from New York at 11 pm with 44 passengers. An hour later, a few passengers got off at New Jersey. The number of passengers who boarded the bus at New Jersey were twice the number of passengers who got off the bus. If the bus has 50 passengers now, how many passengers got off at New Jersey?

#### Let’s define:
Let $ x $ = number of passengers who got off at New Jersey.

Then, number who boarded = $ 2x $ (twice as many).

Initial passengers: 44
After getting off: $ 44 - x $
After boarding: $ (44 - x) + 2x = 44 + x $

We are told that now there are 50 passengers:

$$
44 + x = 50
$$

Solve:
$$
x = 50 - 44 = 6
$$

✔ Answer: 6 passengers got off at New Jersey

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3) Clara lends half her collection of formal attires to her sister, Susan. Clara then buys four more attires. If she has 12 attires now, how many attires did Clara have initially?

Let $ x $ = initial number of attires.

She lent half → she has $ \frac{1}{2}x $ left.

Then she buys 4 more → $ \frac{1}{2}x + 4 = 12 $

Now solve:
$$
\frac{1}{2}x + 4 = 12
$$
Subtract 4:
$$
\frac{1}{2}x = 8
$$
Multiply both sides by 2:
$$
x = 16
$$

✔ Answer: Clara had 16 attires initially

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4) The Rock Zoo nurses 37 species of big cats. Recently, a few species of big cats were sponsored to other zoos around the country. The zoo now nurses only 25 species. How many species of big cats were sponsored to other zoos?

This is straightforward subtraction.

Initially: 37 species
Now: 25 species
So, number sponsored = $ 37 - 25 = 12 $

✔ Answer: 12 species were sponsored

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5) Megan and four of her friends plan to go for a long drive. She buys 12 bottles of frappe and a few bottles of orange juice from a supermarket. The total number of bottles they have are four times that of orange juice bottles. How many bottles of orange juice did Megan buy?

Let $ x $ = number of orange juice bottles.

Total bottles = frappe + orange juice = $ 12 + x $

We're told:
> Total number of bottles = 4 × (number of orange juice bottles)

So:
$$
12 + x = 4x
$$

Solve:
$$
12 = 4x - x \\
12 = 3x \\
x = 4
$$

✔ Answer: Megan bought 4 bottles of orange juice

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✔ Final Answers:

1) 45 marbles
2) 6 passengers got off
3) 16 attires initially
4) 12 species sponsored
5) 4 bottles of orange juice

Let me know if you'd like these written out neatly on the worksheet format!