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3 years ago

Christian and Benjamin go to the movie theater and purchase refreshments for their friends.

Mathematics

1 answer:

maria [59]3 years ago

8 0

Answer:

System of equations:

6d + 3p = 42.75

10d + 15p = 98.75

Drink = $5.75

Popcorn = $2.75

Step-by-step explanation:

6d + 3p = 42.75

subtract 6d from both sides

3p = 42.75 - 6d

divide both sides by 3

p = 14.25 - 2d

substitute P in the second equation with the answer and solve for D

10d + 15( 14.25 - 2d) = 98.75

distribute out the 15

10d + 213.75 -30d = 98.75

-20d + 213.75 = 98.75

subtract 213.75 from both sides

-20d = -115

divide both sides by -20

d = 5.75

substitute D back in the first equation and solve for P

3p + 6(5.75) = 42.75

multiply the 6 and 5.75

3p + 34.5 = 42.75

subtract 34.5 from both sides

3p = 8.25

divide both sides by 3

p = 2.75

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Alicia, Quentin, and Rosalyn are siblings. Alicia is the oldest sibling. Quentin is four years younger than Alicia. Rosalyn is t

tatiyna

Answer:

Alicia is 18years

Quentin is 14years

Rosalyn is 16years

Step-by-step explanation:

Let the age of Alicia be x

Let the age of Quentin be y

Let the age of Rosalyn be z

If the sum of the siblings’ ages, in years, is 48 then;

x+y+z = 48.... 1

If Rosalyn is two years older than Quentin then;

z =y+2 ..... 2

Also if Quentin is four years younger than Alicia then;

y = x-4 ... 3

From 3:

x = y+4 ... 4

Substitute 2 and 4 into 1 to have:

y+4+y+y+2 = 48

3y + 6= 48

3y = 48-6

3y= 42

y = 14

Since x= y+4

x = 14+4

x = 18

Since z = y+2

z = 14+2

z = 16year

This means that;

Alicia is 18years

Quentin is 14years

Rosalyn is 16years

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3 years ago

For Xavier's lemonade recipe, 6 lemons are required to make 4 cups of lemonade. At what rate are lemons being used in cups of le

dusya [7]

Answer:

Since 6 lemons are used to make 4 cups of lemonade, then are used $\frac{6}{4} =\frac{3}{2}$ of lemon per cup of lemonade, or are make $\frac{4}{6}=\frac{2}{3}$ cups of lemonade per lemon.

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3 years ago

5(3-x)-4(2-3x)>2 what is the inequality of x

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Answer:

6547

Step-by-step explanation:

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3 years ago

The table below represents the displacement of a turtle from its nest as a function of time: Time (hours) x Displacement from ne

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Part A: The y-intercept is 5. If you look to the data, when x=0, y=5. This means that the turtle started off 5 miles away from its nest. (at 0 hours, the distance away from his nest was 5 miles)

Part B:Answer=22. Remember, if you take any two distinct points on a line, the slope of the line will be equal to the average rate of change. In short, we're just looking for the slope between the ordered pairs (1,27) and (4,93). The formula for slope is:

$slope= \frac{y_{2}- y_{1} }{ x_{2} - x_{1} } = \frac{93-27}{4-1}= \frac{66}{3}=22$

The average rate of change between x=1 and x=4 is 22. The average rate of changed describes the rate at which miles is changing with respect the the change in hour.

Part C: Answer=10hours. Since by now we know both the slope and the y-intercept, lets write the equation in slope intercept form and then solve for 225 miles.

y=mx+b
y=22x+5
225=22x+5
subtract 5 from both sides
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divide both sides by 22
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