Suzanne can work 10 math problems in 15 minutes. How many can she work in an hour and a half?

A cleaning company charges x dollars per hour to clean floors and y dollars per hour to clean the rest of a house.

saul85 [17]

The answer is B. (15,18)

Solution:

First, let's set the variables first.

X = dollars per hour to clean the floor
Y = dollars per hour to clean the rest of the house

For the first statement, "<span>2 hours to clean floors and 3 hours to clean the rest of a house, the total charge is $84"
We can put it into an equation.
2X + 3Y = 84 </span>⇒ equation 1

For the first statement, "<span>1 hour to clean floors and 4 hours to clean the rest of a house, the total charge is $87'
X + 4Y = 87 </span>⇒ equation 2

Multiply first equation 2 by 2 to make the coefficient of both equations 1 and 2 the same.

Using elimination method in solving for x and y,

   (equation 1)   2X + 3Y = 84
   (equation 2)   2(X + 4Y) = 87
2X + 8Y = 174  ⇒ equation 3

Next, subtract equation 3 from equation 1.
  2X + 3Y = 84
- (2X + 8Y = 174)
-------------------------
- 5Y = -90
Y = 18

Find X when Y = 18
@ equation 1 : 2X + 3Y = 84
2X + 3(18) = 84
2X + 54 = 84
2X = 84 - 54
2X = 30
X = 15

The answer is in ordered pairs of cleaning the floors and to clean the rest of the house. So, in the form (X,Y).

Answer: (15,18)

6 0

3 years ago

Sarah took the advertising department from her company on a round trip to meet with a potential client. Including Sarah a total

Gelneren [198K]

Answer : Sarah bought 4 first class tickets and 3 coach tickets.

Explanation :

We will call F the number of first class tickets and C the number of coach tickets.

Sarah had to buy a total of 7 tickets for 7 people.

Then F + C = 7 (Equation 1)

She used her total budget = $5,620

Then F*$1,150 + C*$340 = $5,620 (Equation 2)

F + C = 7

F = 7 - C

Now we can replace the value F in the equation 2

(7 - C)*$1,150 + C*$340 = $5,620

7*$1,150 - C*$1,150 + C*$340 = $5,620

$8,050 - C*$810 = $5,620

$8,050 - $5,620 = C*$810

$2,430 = C*$810

C = $2,430/$810 = 3 => number of coach tickets

F = 7 - C = 7 - 3 = 4 => number of first class tickets

Answer : Sarah bought 4 first class tickets and 3 coach tickets.

Verification

Replacing these values in equation 2

4*$1,150 + 3*$340 = $4,600 + $1,020 = $5620 => total budget

$\textit{\textbf{Spymore}}$

5 0

3 years ago

Your sister is considering two different shapes for her garden. One is a square with side lengths of 3.5 meter, and the other is

Bess [88]

Hello! I can help you with this!

A. Okay. So, to find the area of the square all you have to do is the number square, or multiply the number by itself, in this case. 3.5. 3.5^2 is 12.25. The area of the square is 12.25 square meters large.

B. To find the area of the circle, you do pi*r^2. Radius is half the the diameter. Half of 4 is 2. 2^2 is 4. To multiply by pi, we can just do it as 3.14. 4 * 3.14 is 12.56. The circle is 12.56 square meters large.

C. The circle garden would give her the most space to plant, because 12.56 is larger than 12.25 by 0.31. The circle garden 0.31 square meters larger than the square garden.

3 0

3 years ago

In a function, an input can have more than one output. True Or False ??

Fudgin [204]

False. For every x in the function's domain, f(x) describes the one single output.

7 0

4 years ago

Max is on a diet.he want to have a snack.he cam have a snack if it less than 220kcal

Ludmilka [50]

500/20 = 25kcal per piece
8 * 25 = 200kcal.....yes, he is able to have 8 pieces

4 0

4 years ago