Answer:
Paula = 4 hours
Roberto = 12 hours
Step-by-step explanation:
Time taken by Paula = x
Time taken by Roberto = x +. 8
Paula's rate = 1/x
Roberto's rate = 1/(x + 8)
Combined rate = 1/3
Time it takes each if them working alone ;
Paula's rate + Roberto's rate = combined rate
1 /x + 1 / (x +8) = 1/3
Take the L. C. M
((x+8) + x) / x(x+8) = 1/3
(2x + 8) / x(x + 8) = 1/3
3(2x + 8) = x(x + 8)
6x + 24 = x² + 8x
x² + 8x - 6x - 24 = 0
x² + 2x - 24 = 0
Solving the quadratic equation :
x² + 6x - 4x - 24 = 0
x(x + 6) - 4(x + 6) = 0
(x - 4) = 0 or (x + 6) = 0
x = 4 or x = - 6
Time taken cannot be negative
Hence, x = 4
Hence, working alone, it takes ;
Time taken by Paula = 4
Time taken by Roberto = 4 + 8 = 12
Just substitute 1 as the value and you will get your answer
9514 1404 393
Answer:
Step-by-step explanation:
Let a and s represent the prices of adult and student tickets, respectively.
13a +12s = 211 . . . . . . ticket sales the first day
5a +3s = 65 . . . . . . . ticket sales the second day
Subtracting the first equation from 4 times the second gives ...
4(5a +3s) -(13a +12s) = 4(65) -(211)
7a = 49 . . . . . . . simplify
a = 7 . . . . . . . divide by 7
5(7) +3s = 65 . . . . substitute into the second equation
3s = 30 . . . . . . . subtract 35
s = 10 . . . . . . . divide by 3
The price of one adult ticket is $7; the price of one student ticket is $10.
Given:
May:
hamburger: 3.2 pounds * 4.25 = 13.60
hotdogs: 3 packages * 4 = 12
Total cost: 13.60 + 12 = 25.60
June:
hamburger: 3.2 pounds * 1 1/2 = 4.8 pounds * 4.25 = 20.4
hotdogs: 3 packages * 1/3 = 1 package * 4 = 4
Total cost: 20.4 + 4 = 24.4
25.60 - 24.40 = 1.20
They spent more on May by $1.20. Choice C.
