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Lidia is paid at a standard rate per hour before 5 pm, and then a higher rate per hour after 5 pm. On Monday she worked from 2 pm to 7 pm and earned $110. On Tuesday she worked from 11 am to 8 pm and earned $195. On Wednesday lidia worked from noon to 6 pm. How much did she earn on Wednesday?

Respuesta :

reinhard10158

Step-by-step explanation:

x = standard rate

y = higher rate

Monday : 2pm to 7pm

that means 2pm to 5pm and 5pm to 7pm.

3 hours (2 to 5) standard, 2 hours (5 to 7) high.

so,

3x + 2y = 110

Tuesday : 11am to 8pm

that means 11am to 5pm and 5pm to 8pm.

6 hours (11am to 5) standard, 3 hours (5 to 8) high.

so,

6x + 3y = 195

that gives us 2 equations in 2 variables.

3x + 2y = 110

6x + 3y = 195

multiply the first by -2 and add :

-6x - 4y = -220

6x + 3y = 195

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

0 - y = -25

y = 25

use e.g. the first original equation to get now x :

3x + 2×25 = 110

3x + 50 = 110

3x = 60

x = 20

so, Wednesday : 12pm to 6pm.

that means 12pm to 5p and 5pm to 6pm.

5 hours (12pm to 5) standard, 1 hour (5 to 6) high.

so,

5x + y = 5×20 + 25 = 100 + 25 = $125

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