Printable math worksheet with five two-step integer equation word problems for practice.

Let's solve each problem step by step.

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Problem 1:

Dalia bought a few swirl marbles and divided them 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 Dalia bought in all.

#### Solution:
1. Let the total number of marbles Dalia bought be \( x \).
2. Dalia divided the marbles equally among 5 people (4 friends + 1 brother, Jake).
- Therefore, each person received \( \frac{x}{5} \) marbles.
3. Jake initially had \( \frac{x}{5} \) marbles.
4. Jake lost 2 marbles and now has 7 marbles.
- This gives us the equation: \( \frac{x}{5} - 2 = 7 \).
5. Solve for \( x \):
\[
\frac{x}{5} - 2 = 7
\]
Add 2 to both sides:
\[
\frac{x}{5} = 9
\]
Multiply both sides by 5:
\[
x = 45
\]

#### Answer:
\[
\boxed{45}
\]

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Problem 2:

A bus departed from New York at 11 am 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 was twice the number of passengers who got off. If the bus has 50 passengers now, how many passengers got off at New Jersey?

#### Solution:
1. Let the number of passengers who got off at New Jersey be \( y \).
2. The number of passengers who boarded the bus at New Jersey is \( 2y \) (twice the number who got off).
3. Initially, the bus had 44 passengers.
4. After some passengers got off and others boarded, the bus now has 50 passengers.
- This gives us the equation:
\[
44 - y + 2y = 50
\]
5. Simplify the equation:
\[
44 + y = 50
\]
6. Solve for \( y \):
\[
y = 50 - 44
\]
\[
y = 6
\]

#### Answer:
\[
\boxed{6}
\]

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Problem 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 initially have?

#### Solution:
1. Let the initial number of attires Clara had be \( x \).
2. Clara lends half of her attires to Susan, so she is left with \( \frac{x}{2} \) attires.
3. Clara then buys 4 more attires, so the total number of attires she has now is:
\[
\frac{x}{2} + 4
\]
4. According to the problem, Clara now has 12 attires:
\[
\frac{x}{2} + 4 = 12
\]
5. Solve for \( x \):
\[
\frac{x}{2} + 4 = 12
\]
Subtract 4 from both sides:
\[
\frac{x}{2} = 8
\]
Multiply both sides by 2:
\[
x = 16
\]

#### Answer:
\[
\boxed{16}
\]

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Problem 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?

#### Solution:
1. Let the number of species sponsored to other zoos be \( y \).
2. Initially, the zoo nursed 37 species.
3. After sponsoring some species, the zoo now nurses 25 species.
- This gives us the equation:
\[
37 - y = 25
\]
4. Solve for \( y \):
\[
37 - y = 25
\]
Subtract 25 from both sides:
\[
y = 37 - 25
\]
\[
y = 12
\]

#### Answer:
\[
\boxed{12}
\]

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Problem 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?

#### Solution:
1. Let the number of bottles of orange juice be \( y \).
2. Megan bought 12 bottles of frappe.
3. The total number of bottles is the sum of frappe bottles and orange juice bottles:
\[
12 + y
\]
4. According to the problem, the total number of bottles is four times the number of orange juice bottles:
\[
12 + y = 4y
\]
5. Solve for \( y \):
\[
12 + y = 4y
\]
Subtract \( y \) from both sides:
\[
12 = 3y
\]
Divide both sides by 3:
\[
y = 4
\]

#### Answer:
\[
\boxed{4}
\]

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Final Answers:

1. \(\boxed{45}\)
2. \(\boxed{6}\)
3. \(\boxed{16}\)
4. \(\boxed{12}\)
5. \(\boxed{4}\)