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10. Dor 13 in thi Gopal and Henry were paid a total of $3850 for a job they did. Gopal was paid $2030 more than Henry. (a) How much was Gopal paid for the job? (b) Gopal and Henry were paid based on the number of days they worked. Gopal worked 3 times as many days as Henry. Gopal was paid $5 more than Henry per day. How many days did Gopal work?

Respuesta :

Answer:

a) The amount paid to Gopal was $2940

and, the amount paid to Henry was $910

b) number of days worked by Gopal  = 42

Step-by-step explanation:

Given:

Total amount paid = $3850

let the amount paid to Henry was 'x' and the amount paid to Gopal be 'y'

Thus according to the question

y = x + $2030 .............(1)

also,

x + y = $3850 ...........(2)

substituting the value of y in the equation (2), we get

x + x + $2030 = $3850

or

2x = $3850 - $2030

or

2x = $1820

or

x = $910

substituting the value of x in equation (1), we get

y =  $910 + $2030 = $2940

a) Hence, the amount paid to Gopal was y = $2940

and, the amount paid to Henry was x = $910

b) let amount paid per day to Henry was 'h'

therefore,

amount paid to Gopal = h + $5

and,

the number of days worked by Henry be d

therefore,

the number of days worked by Gopal = 3d

also,

3d × ( h + $5 ) = $2940  

or

3dh + 15d = $2940    ..............(3)

and,

d × h = $910  ..........(4)

substituting (4) in the equation (3), we get

3 × 910 + 15d = $2940  

or

15d = $2940 - $2730

or

15d = $210

or

d = 14

and, number of days worked by Gopal = 3d = 3 × 14 = 42

Hence,

number of days worked by Gopal  = 42

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