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Chapter 1: Problem 5

If \(20 \%\) of a shipment of 50,000 tomatoes is crushed during transport and then \(5 \%\) of the remaining tomatoes are lost to insects, then how many tomatoes remain?

Short Answer

Expert verified
First, calculate the number of crushed tomatoes during transport: \(50,000 \times 20\% = 10,000\) tomatoes. Then, find the remaining tomatoes after transport: \(50,000 - 10,000 = 40,000\) tomatoes. Next, calculate the number of tomatoes lost to insects: \(40,000 \times 5\% = 2,000\) tomatoes. Finally, find the total remaining tomatoes: \(40,000 - 2,000 = 38,000\) tomatoes. Therefore, \(38,000\) tomatoes remain.

Step by step solution

01

Find the number of tomatoes crushed during transport

To find out how many tomatoes are crushed during transport, we have to calculate 20% of 50,000. This can be written in the form of a simple percentage formula: Crushed tomatoes = Total Tomatoes × Percentage of crushed tomatoes
02

Calculate the remaining tomatoes after transport

To calculate the remaining tomatoes after transport, we have to subtract the number of crushed tomatoes from the total tomatoes: Remaining tomatoes = Total tomatoes - Crushed tomatoes
03

Find the number of tomatoes lost to insects

To find out how many tomatoes are lost to insects from the remaining tomatoes after transport, we have to calculate 5% of the remaining tomatoes. This can be written in the form of a simple percentage formula: Tomatoes lost to insects = Remaining tomatoes × Percentage of tomatoes lost to insects
04

Calculate the final remaining tomatoes

To calculate the final remaining tomatoes, we have to subtract the number of tomatoes lost to insects from the remaining tomatoes after transport: Final remaining tomatoes = Remaining tomatoes - Tomatoes lost to insects Now, let's plug in the numbers and find the solution.
05

Find the number of tomatoes crushed during transport

Crushed tomatoes = 50,000 × 20% = 50,000 × 0.2 = 10,000 tomatoes
06

Calculate the remaining tomatoes after transport

Remaining tomatoes = 50,000 - 10,000 = 40,000 tomatoes
07

Find the number of tomatoes lost to insects

Tomatoes lost to insects = 40,000 × 5% = 40,000 × 0.05 = 2,000 tomatoes
08

Calculate the final remaining tomatoes

Final remaining tomatoes = 40,000 - 2,000 = 38,000 tomatoes So, 38,000 tomatoes remain after transport and insect losses.

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