Question

write a word problem that can be solved using a system of two linear equations. solve the problem and give the meaning of the answer.

Answer 1

The sum of two numbers is 25. One of the numbers exceeds the other by 9. Find numbers

here

the other number = x + 9

Let the number be x.

Sum of two numbers = 25

According to question, x + x + 9 = 25

⇒ 2x + 9 = 25

⇒ 2x = 25 - 9

⇒ 2x = 16

⇒ 2x/2 = 16/2

⇒ x = 8

Therefore, x + 9 = 8 + 9 = 17

Therefore, the two numbers are 8 and 17.

Answer 2

Fritz wants to get a job to save up money for college, he has two options:

Mr. Smith's Bakery or Samantha's Ice Cream Shop

Mr. Smith's Bakery is close to Fritz's house so he can walk to it, it pays $8.00 per hour. Samantha's Ice Cream Shop is a bit farther away so Fritz has to pay $4 for bus fare every day, the pay is $10.00 per hour.

How long would Fritz have to work at Samantha's Ice Cream Shop to get the same amount at Mr. Smith's Bakery?

In this system, x is the number of hours worked and y is the total amount earned.

Bakery: y = 8x

Ice Cream: y = 10x-4

Solve for x using substitution

8x=10x-4

2x=4

x=2, This means that it will take 2 hours of work to get the same amount of pay.