1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
fenix001 [56]
3 years ago
9

The total number of​ restaurant-purchased meals that the average person will eat in a​ restaurant, in a​ car, or at home in a ye

ar is 152. The total number of these meals eaten in a car or at home exceeds the number eaten in a restaurant by 12. Ten more​ restaurant-purchased meals will be eaten in a restaurant than at home. Find the number of​ restaurant-purchased meals eaten in a​ restaurant, the number eaten in a​ car, and the number eaten at home.
Mathematics
1 answer:
zloy xaker [14]3 years ago
8 0

Answer:

Number of​ restaurant-purchased meals eaten in a​ restaurant = 70

Number of​ restaurant-purchased meals eaten in a​ car = 22

Number of​ restaurant-purchased meals eaten in a​ home = 60

Step-by-step explanation:

Let the number of people that will eat in a restaurant be R.

Let the number of people that will eat in a car be C.

Let the number of people that will eat in a home be H.

From the information given in the problem we have,

R+C+H = 152 ____equation (1)

C+H-R = 12 ____equation (2)

R = H+10 ____equation (3)

1) Plugging in R=H+10 from equation 3 into the equation 2, we get

C+H-R=12

=> C+H-(H+10)=12

=> C+H-H-10=12

2) Cancelling out +H and -H, we get

C-10=12

3) Add 10 to both sides

C-10+10=12+10

4) Cancelling out -10 and +10, we get

C=22

5) Plugin C=22 in equation 1, we have

R+C+H = 152

=> R+22+H=152

Subtract 22 from both sides,

R+22+H-22=152-22

Cancelling out +22 and -22 from the left side, we get

R+H=130 ____let it be equation (4)

6) Plugin C=22 in equation 2, we have

C+H-R = 12

22+H-R = 12

Subtracting 22 from both the sides, we get

22+H-R-22 = 12-22

Cancelling out +22 and -22 from the left side,

H-R = -10 ____let it be equation (5)

7) Adding equation 4 and equation 5, we get

(R+H)+(H-R) = 130 + (-10)

=> R+H+H-R = 130-10

8) Cancelling out R and -R from the left side, we get

2H = 120

9) Dividing both sides by 2, we get

\frac{2H}{2} = \frac{120}{2}

10) Cancelling out the 2's from the left side, we have

H=60

11) Plugging in C=22 and H=60 in the equation 1, we have

R+C+H = 152

=> R+22+60=152

=> R + 82 = 152

12) Subtracting 82 from both the sides, we get

R + 82 -82 = 152 -82

13) Cancelling out +82 and -82 from the left side, we get

R = 70

<em>So, C=22, H=60, R=70</em>

You might be interested in
120 is 15% of what number
son4ous [18]
120 = 15% x

15% = 0.15

x = 120 / 0.15 = 800
6 0
3 years ago
Read 2 more answers
Which sequences of transformations will map circle<br><br> M onto circle N?
sergiy2304 [10]

Answer:

1: Reflect M across the x-axis

2: Dilate about the center by 3/2

Step-by-step explanation:

Given

See attachment for M and N

Required

Which maps M to N

The coordinates of the radius of the circles are:

M = (5,5)

N = (5,-5)

And the radius of circles are:

r_M=2

r_N=3

The first transformation from M to M' is:

- Reflect across the x-axis

The rule is:

(x,y) \to (x,-y)

M(5,5) \to M'(5,-5)

<em>At this point, M' and N now have the same center but different radius.</em>

The second transformation from M' to N is:

- Dilate about the center by dividing the radius of N by the radius of M

i.e.

k =\frac{r_N}{r_M}

k =\frac{3}{2}

<em>At this point, M has been completely mapped to N.</em>

4 0
3 years ago
The perimeter of a scalene triangle is 14.5 cm. The longest side is twice that of the shortest side. Which equation can be used
Deffense [45]
3,1 centimetrs (three, point, one)
4 0
3 years ago
Read 2 more answers
Simon pays $9 for 6 visits to swim at the community pool. He pays $18 for 12 visits to swim. How much does it cost for each visi
sergij07 [2.7K]

Answer:

$1.50

Step-by-step explanation:

If you do cost per quantity you would get $9 over 6 visits. Then you divide both sides by 6 because to get to one by 6 it's 6 so when you divide both sides by 6 you would get 1.5 over 1 and all you do is add a zero because you're dealing with money

Hope this helps :)

8 0
3 years ago
13 + 5x - 4y - 8<br> .<br> I need to simplify the expression
IrinaK [193]

Answer:

5+5x-4y

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • What is the measure on an interior angle of this polygon?
    6·2 answers
  • Someone please help this is on a test
    15·2 answers
  • 1. If Kenya's total debt to her parents is five
    9·1 answer
  • What is the point slope equation of the line with slope -12 that goes through the point (5,3)
    8·1 answer
  • A credit card company requires that its customers choose a 3 digit, numerical code to access their online account. Each digit sh
    15·1 answer
  • What is the slope of the line that passes through the points (-4,8) qnd (-14,8)
    6·2 answers
  • Simplify (4x - 6) + (3x + 6)
    8·2 answers
  • What is the simplified form of 114?<br> A. i<br> B. -1<br> C. 1<br> D. -1
    15·2 answers
  • Anyone knows what 9x323 is? pls I need ASAP
    13·2 answers
  • PLEASE HELP ASAP
    7·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!