Jeremiah and Tristan work at a dry cleaners ironing shirts. Jeremiah can iron 35 shirts per hour, and Tristan can iron 20 shirts per hour. Jeremiah and Tristan worked a combined 17 hours and ironed 490 shirts. Determine the number of hours Jeremiah worked and the number of hours Tristan worked.

The number of hours Jeremiah worked and the number of hours Tristan worked will be 10 hours and 7 hours respectively.

Let Jeremiah worked x hours and Tristan worked y hours.

Given,

Jeremiah can iron 35 shirts per hour.

So no of shirts iron in x hours will be

Tristan can iron 20 shirts per hour.

So, no.of shirts iron in y hours will be .

Now according to the question,Jeremiah and Tristan worked a combined 17 hours so,

Again, Jeremiah and Tristan worked together and ironed 490 shirts. so

or it can be written as,

Now multiplying equation (1) by 7 we get

Now, subtracting equation (2) from equation (3) we get,

Putting the value of y in equation (1), we get

Thus Jeremiah worked for 10 hours and Tristan worked for 7 hours.

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The number of hours Jeremiah ironed = 10 hours

The number of hours Tristan ironed = 7 hours

Step-by-step explanation:

Let 'x' be the number of hours Jeremiah ironed.

Let 'y' be the number of hours Tristan ironed.

x+y = 17   (1)

35x + 20y = 490  (2)

Multiply (1) by 20 and subtract (2) from (1),

 20x + 20y = 340

-(35x + 20y = 490)

 -15x         = -150

x = 150/15

x = 10

Substitute x=10 in (1)

10+y = 17

y = 7