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nexus9112 [7]
3 years ago
12

Maria can clean the entire house in two hours. Her sister, Sasha, can clean the house in three hours. How long would it take for

two of them to do the job together?
Mathematics
1 answer:
MAXImum [283]3 years ago
6 0

72 minutes

We require their hourly rate of work

Maria cleans \frac{1}{2} the house in 1 hour

Sasha cleans \frac{1}{3} of the house in 1 hour

let x be the time it takes both to clean the house

\frac{1}{2} + \frac{1}{3} = \frac{1}{x}

multiply through by 6x

3x + 2x = 6

5x = 6 ⇒ x = \frac{6}{5}

Together they can clean the house in 72 minutes






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The ten students in a club are lined up in a row for a group photograph. How many different arrangements are possible if the clu
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Find the dimensions of a rectangular prism whose volume is (x^4 ‒ y ^4) units3.
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Tickets to a concert cost $2 for children, $3 for teenagers and $5 for adults. When 570 people attended the concert, the total t
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Answer: 220

<u>Step-by-step explanation:</u>

Children (x): $2

Teens (y): $3, \frac{3}{4}x

Adults: (z): $5

Quantity: x + y + z = 570  ⇒  x + \frac{3}{4}x + z = 570  ⇒ 1.75x + z = 570  

Cost: 2x + 3y + 5z = 1950  ⇒  2x + 3(\frac{3}{4}x) + 5z = 1950  ⇒  2x + 2.25x + 5z = 1950  ⇒  4.25x + 5z = 1950

Qty:    1.75x +  z =  570  →  5(1.75x +  z =  570)  →    8.75x + 5z = 2850

Cost: 4.25x + 5z = 1950 → -1(4.25x + 5z = 1950 → <u> -4.25x - 5z</u> = <u>-1950 </u>

                                                                                  4.50x        =   900

                                                                                          x       =    200

Teens (y): \frac{3}{4}x

           y = \frac{3}{4}(200)

             = \frac{600}{4}

             = 150

Quantity: x + y + z = 570  

              200 + 150 + z = 570

                     350     + z = 570

                                    z = 220


6 0
3 years ago
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