Question

The total amount of money earned by all three plumbers on Monday was $1,400. On Tuesday they earned a total of $1,660, and on Wednesday, they earned a total of $1,650. On Thursday, Plumber A made four house calls, Plumber B made six house calls, and Plumber C made three house calls. How much total money is earned on Thursday?

Answer 1

Total money earned on Thursday is $1090.

Explanation:

Let amount of money for one house call of Plumber A be x

So, amount of money for 2 house call of Plumber A=2 x

So, amount of money for 4 house call of Plumber A=4 x

So, amount of money for 3 house call of Plumber A=3 x

Let amount of money for one house call of Plumber B be y

So, amount of money for 8 house call of Plumber B=8 y

So, amount of money for 7 house call of Plumber B=7 y

So, amount of money for 9 house call of Plumber B=9 y

Let amount of money for one house call of Plumber C be z

So, amount of money for 8 house call of Plumber C=8 z

So, amount of money for 10 house call of Plumber C=10 z

So, amount of money for 9 house call of Plumber C=9 z

Now we are given that The total amount of money earned by all three plumbers on Monday was $1,400.

On Monday Plumber A has 2 calls , Plumber B has 8 calls and Plumber C has 8 calls

So, equation becomes:
`2x+8y+8z=1400` --1

On Tuesday they earned a total of $1,660,On Tuesday Plumber A has 4 calls , Plumber B has 7 calls and Plumber C has 10 calls.

So, equation becomes:
`4x+7y+10z=1660` ---2

On Wednesday, they earned a total of $1,650.On Wednesday Plumber A has 3 calls , Plumber B has 9 calls and Plumber C has 9 calls.

So, equation becomes:
`3x+9y+9z=1650` ----3

Solving equation 1 ,2 AND 3

Equation 3:
`3x+9y+9z=1650`

`x+3y+3z=550` ---4

Now substitute the value of x from 4 in 1 and 2

`2(550-3y-3z)+8y+8z=1400` and
`4(550-3y-3z)+7y+10z=1660`

`1100-6y-6z+8y+8z=1400` and
`2200-12y-12z+7y+10z=1660`

`2y+2z=300` --- (a) and
`5y+2z=540`---(b)

Now substitute the value of y from a in b

`5((300-2z)/(2))+2z=540`

`5(150-z)+2z=540`

`750-5z+2z=540`

`750-3z=540`

`210=3z`

`70=z`

Substitute the value of z in (a)

`2y+2(70)=300`

`2y+140=300`

`2y=160`

`y=80`

Substitute the value of y and z in 1

`2x+8(80)+8(70)=1400`

`2x+640+560=1400`

`2x+1200=1400`

`2x=200`

`x=100`

So, amount of money for one house call of Plumber A = $100

So, amount of money for one house call of Plumber B =$80

So, amount of money for one house call of Plumber C =$70

On Thursday Plumber A made four house calls, Plumber B made six house calls, and Plumber C made three house calls.

So, equation becomes :
`4x+6y+3z`

Substitute the values of x ,y and z

`4(100)+6(80)+3(70)`

`400+480+210`

`1090`

Thus total money earned on Thursday is $1090.

Hence Option C is correct.

Answer 2

Set of equations that can be used to calculate rate for each plumber:
2A+8B+8C = 1,400 --- (1)
4A+7B+10C = 1,660 --- (2)
3A+9B+9C = 1,660 --- (3)
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2*(1) - (2)
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4A+16B+16C = 2,800
4A+7B+10C = 1,660 -
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9B+6C = 1,140 --- (4)
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3(2) -4(3)
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12A+21B+30C = 4,980
12A+36B+36C = 6,600 -
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-15B-6C = -1,620 --- (5)
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(4) + (5)
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9B+6C = 1140
-15B-6C = -1620 +
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-6B = -480 => 6B = 480 => B = 480/6 = 80
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Using (4), 9(80)+6C = 1140
720+6C = 1140 => 6C = 1140-720 = 420 => C = 420/6 = 70
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Using (1), 2A+8(80)+8(70) = 1400
2A+640+560 =1400 => 2A = 1400-640-560 = 200 => A = 200/2 = 100
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The rates are:
A = $100
B = $80
C = $70
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On Thursday, number of calls: A = 4 hrs, B = 6 hrs, C = 3 hrs
Money earned = 4*100+6*80+3*70 = $1,090