Mindy, Daisy, Araceli and Leigh worked together on a job. The job paid $220. Each person was paid according to the amount of work they contributed to the job. Daisy and Araceli earned $280 together. Daisy and Mindy have $260, and Daisy and Leigh got $220. What percent of the job did each person do
M+D+A+L = 4(220) = 880 (#1)
D+A = 280 ---> A = 280-D
D+M = 260 ---> M = 260-D
D+L = 220 ---> L = 220-D
in #1
260-D + D + 280-D + 220-D = 880
-2D = 120
D = -60
which makes no sense!
but.... let's keep going
then
A = 280-(-60) = 340
D = -60
M = 260-(-60) = 320
L = 220-(-60) = 280
check: 340 - 60 + 320 + 280 = indeed 880
But you can't earn negative dollars
bogus question!!!!
tank you very much
To determine the percentage of the job each person did, we need to first find the individual earnings and then compare them to the total earnings.
Let's assign variables to each person's earnings:
- Mindy's earnings: M
- Daisy's earnings: D
- Araceli's earnings: A
- Leigh's earnings: L
From the given information, we have the following equations:
1. Daisy and Araceli earned $280 together:
D + A = $280
2. Daisy and Mindy earned $260:
D + M = $260
3. Daisy and Leigh earned $220:
D + L = $220
We can solve these equations simultaneously to find the individual earnings:
From equations (2) and (3), we can subtract D from both sides of each equation:
M = $260 - D
L = $220 - D
Now, substitute these values into equation (1):
D + A = $280
D + ($260 - D) + ($220 - D) = $280
Simplify the equation:
$260 - D + $220 - D = $280
$480 - 2D = $280
Subtract $480 from both sides:
-2D = $280 - $480
-2D = -$200
Divide both sides by -2:
D = $200 / 2
D = $100
Now, let's substitute this value back into equations (2) and (3) to find the other earnings:
From equation (2):
M + $100 = $260
M = $260 - $100
M = $160
From equation (3):
L + $100 = $220
L = $220 - $100
L = $120
Now that we have the individual earnings, we can calculate the percentage of the job each person did:
Mindy's percentage:
M / $220 * 100% = $160 / $220 * 100% ≈ 72.73%
Daisy's percentage:
D / $220 * 100% = $100 / $220 * 100% ≈ 45.45%
Araceli's percentage:
A / $220 * 100% = (job earnings - Daisy's earnings) / $220 * 100% = ($220 - $100) / $220 * 100% ≈ 54.55%
Leigh's percentage:
L / $220 * 100% = $120 / $220 * 100% ≈ 54.55%
Therefore, the percentage of the job each person did is approximately:
- Mindy: 72.73%
- Daisy: 45.45%
- Araceli and Leigh: 54.55%