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V125BC [204]
3 years ago
12

Working his way through school, Joe works two part-time jobs for a total of 18 hours a week. Job A pays $5.70 per hour, and Job

B pays $6.80 per hour. How many hours did he work at each job the week that he made $111.40?
Mathematics
2 answers:
ad-work [718]3 years ago
4 0

Answer:

A = 14.2/1.1 hours

B = 5.091 hours

Step-by-step explanation:

Formulate 2 simultaneous equations

5.7A + 6.8B = 111.40..........(1)

A +B =18...............................(2)

Multiply each item in (2) by 5.7 to get

5.7A + 5.7B = 97.2............(3)

subtract (1) - (3) on each side

5.7A -5.7A + 6.8B - 5.7B = 111.40 -97.2

1.1B = 14.2

B = 14.2 /1.1

to get A use equation (2)

A = 18 - B

A = 18 - 14.2/1.1 = 5.091

kirill [66]3 years ago
3 0

Answer:in the week , he worked 10 hours at Job A and 8 hours at job B

Step-by-step explanation:

Let x represent the number hours that Joe worked at job A in a week.

Let y represent the number of hours that Joe worked at job B in a week.

Working his way through school, Joe works two part-time jobs for a total of 18 hours a week. This means that

x + y = 18

Job A pays $5.70 per hour, and Job B pays $6.80 per hour. He made a total of $111.4 working at each job during the week. It means that

5.7x + 6.8y = 111.4 - - - - - - - - - -1

Substituting x = 18 - y into equation 1, it becomes

5.7(18 - y) + 6.8y = 111.4

102.6 - 5.7y + 6.8y = 111.4

- 5.7y + 6.8y = 111.4 - 102.6

1.1y = 8.8

y = 8

x = 18 - y = 18 - 8

x = 10

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Nick was surveying his field and saw some cows and ducks. Nick counted a total of 80 heads and
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Answers:

  • Total equation:  x+y = 80
  • Legs equation:  2x+4y = 248
  • How many ducks? 36
  • How many cows? 44

====================================================

Further explanation:

  • x = number of ducks
  • y = number of cows

x+y = 80 is the total equation (ie the head count equation) since we assume each animal has 1 head, and there are 80 heads total.

That equation can be solved to y = 80-x after subtracting x from both sides.

The legs equation is 2x+4y = 248 because...

  • 2x = number of legs from all the ducks only
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  • 2x+4y = total number of legs from both types of animals combined

We're told there are 248 legs overall, so that's how we ended up with 2x+4y = 248

------------

Let's plug y = 80-x into the second equation and solve for x.

2x+4y = 248

2x+4( y ) = 248

2x+4( 80-x ) = 248

2x+320-4x = 248

-2x+320 = 248

-2x = 248-320

-2x = -72

x = -72/(-2)

x = 36

There are 36 ducks

Now use this x value to find y

y = 80-x

y = 80-36

y = 44

There are 44 cows.

------------

Check:

36 ducks + 44 cows = 80 animals total

36*2 + 44*4 = 72 + 176 = 248 legs total

The answers are confirmed.

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y = 24/3

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x = 8 - 3

x = 5

Therefore, the first number is 5 and the second number is 8.

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