Question

A professional organizer charges an AED 10 consultation fee, plus AED 5 per hour. Her competitor charges an AED 11 consultation fee, plus AED 4 per hour.

Write and solve a system of equations to find the number of hours that the total charge will be the same. What will that charge be?

Enter the correct answer into the blank.

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Answer 1

Answer: Let's let x be the number of hours worked. Then, the total charge for the first organizer is:

10 + 5x

The total charge for the second organizer is:

11 + 4x

To find the number of hours where the total charges are the same, we can set these two expressions equal to each other:

10 + 5x = 11 + 4x

Subtracting 4x from both sides gives:

10 + x = 11

Subtracting 10 from both sides gives:

x = 1

So the number of hours where the total charges are the same is 1 hour. To find the charge at that time, we can substitute x = 1 into either expression. Let's use the first organizer's expression:

10 + 5x = 10 + 5(1) = 15

So the charge at 1 hour is AED 15.

Explanation: