Mark works two jobs - he works in Bob’s Bakery and in Ciara’s Café. He is paid €11.50 an hour for his work in Bob’s Bakery, and €9.30 an hour for his work in Ciara’s Café. In one week he worked a total of 34 hours and was paid a total of €362.40. Find how many hours he worked in Bob’s Bakery in this week.

Junior Cycle Mathematics ALGEBRA: Mark works two jobs

Mark works two jobs - he works in Bob’s Bakery and in Ciara’s Café - Junior Cycle Mathematics - Question 7 - 2012

Question 7

Mark works two jobs - he works in Bob’s Bakery and in Ciara’s Café. He is paid €11.50 an hour for his work in Bob’s Bakery, and €9.30 an hour for his work in Ciara’s... show full transcript

Worked Solution & Example Answer:Mark works two jobs - he works in Bob’s Bakery and in Ciara’s Café - Junior Cycle Mathematics - Question 7 - 2012

Step 1

Let b be the hours that Mark worked in Bob's Bakery, and y be the hours that Mark worked in Ciara's Café.

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Answer

We know that the total hours worked in a week is 34, so we have the equation:

$x + y = 34$

In addition, based on the pay rates from both establishments and the total amount earned, we have:

$(11.5)x + (9.3)y = 362.40$

Step 2

Solve these equations simultaneously:

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Answer

We can solve the first equation for y:

$y = 34 - x$

Now, substitute this into the second equation:

$(11.5)x + (9.3)(34 - x) = 362.40$

Step 3

Distribute and simplify the equation:

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Answer

Expanding the equation gives:

$11.5x + 316.2 - 9.3x = 362.40$ Combine like terms:

$(11.5 - 9.3)x + 316.2 = 362.40$

which simplifies to:

$2.2x + 316.2 = 362.40$

Step 4

Isolate x:

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Answer

Subtract 316.2 from both sides:

$2.2x = 362.40 - 316.2$

Calculating this results in:

$2.2x = 46.2$

Step 5

Find the value of x:

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Answer

Now, divide both sides by 2.2:

$x = rac{46.2}{2.2} = 21$

Thus, Mark worked 21 hours in Bob's Bakery.

Mark works two jobs - he works in Bob’s Bakery and in Ciara’s Café - Junior Cycle Mathematics - Question 7 - 2012

Worked Solution & Example Answer:Mark works two jobs - he works in Bob’s Bakery and in Ciara’s Café - Junior Cycle Mathematics - Question 7 - 2012

Let b be the hours that Mark worked in Bob's Bakery, and y be the hours that Mark worked in Ciara's Café.

Solve these equations simultaneously:

Distribute and simplify the equation:

Isolate x:

Find the value of x:

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