Word Problems With Mixed Operations - Free Printable

Let's solve each of the mixed operations word problems step by step and explain the reasoning.

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Given Information:

- Normal day: 280 planes take off
- Christmas holidays: 336 planes take off per day
- Airport operates 12 hours during Christmas holidays

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Problem 1:

> During the Christmas holidays, the airport opens 12 hours during each day. How many planes take off from this airport in each hour?

Solution:

We are told that 336 planes take off in 12 hours, so we divide total planes by number of hours:

$$
\frac{336}{12} = 28
$$

✔ Answer: 28 planes take off each hour during Christmas holidays.

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Problem 2:

> In average, each plane takes 240 passengers and 12 tons of cargo. How many passengers depart from the airport every hour during the Christmas holidays?

We already know from Problem 1 that 28 planes take off per hour during Christmas.

Each plane carries 240 passengers, so:

$$
28 \text{ planes/hour} \times 240 \text{ passengers/plane} = 6,720 \text{ passengers/hour}
$$

✔ Answer: 6,720 passengers depart every hour during Christmas holidays.

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Problem 3:

> Compared with a normal day, how many more passengers depart from the airport in a day during the Christmas holidays?

First, calculate passengers on a normal day:
- 280 planes × 240 passengers = $ 280 \times 240 $

$$
280 \times 240 = (28 \times 24) \times 100 = 672 \times 100 = 67,200 \text{ passengers}
$$

Now, Christmas holiday day:
- 336 planes × 240 passengers = $ 336 \times 240 $

Break it down:
$$
336 \times 240 = 336 \times (200 + 40) = (336 \times 200) + (336 \times 40)
$$
$$
= 67,200 + 13,440 = 80,640 \text{ passengers}
$$

Now find the difference:
$$
80,640 - 67,200 = 13,440
$$

✔ Answer: 13,440 more passengers depart during Christmas holidays compared to a normal day.

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Problem 4:

> During a normal day, there are 782 passengers late for their plane each day. During Christmas holidays, there are 1,835 late passengers. How many more passengers are late during Christmas holidays?

Subtract:
$$
1,835 - 782 = 1,053
$$

✔ Answer: 1,053 more passengers are late during Christmas holidays.

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Problem 5:

> An additional 5 minutes of delay is caused for every 32 late passengers. If there are 832 late passengers, what is the total delay?

We need to find how many groups of 32 are in 832:

$$
\frac{832}{32} = 26
$$

Each group causes 5 minutes of delay, so:
$$
26 \times 5 = 130 \text{ minutes}
$$

✔ Answer: The overall operation is delayed by 130 minutes.

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Problem 6:

> Write an equation using “x” and then solve.
>
> On New Year’s Eve, 7,580 tons of cargo were loaded in the morning. In the afternoon, x tons were loaded. Total cargo was 12,997 tons.

Step 1: Set up the equation

$$
\text{Morning cargo} + \text{Afternoon cargo} = \text{Total cargo}
$$
$$
7,580 + x = 12,997
$$

Step 2: Solve for x

$$
x = 12,997 - 7,580 = 5,417
$$

✔ Answer: $ x = 5,417 $ tons

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✔ Final Answers Summary:

1. 28 planes per hour
2. 6,720 passengers per hour
3. 13,440 more passengers per day
4. 1,053 more late passengers per day
5. 130 minutes delay
6. Equation: $ 7,580 + x = 12,997 $ → $ x = 5,417 $

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