Answer:
They buy 6 hotdogs and 5 popcorn
Step-by-step explanation:
Assume that they buy x hotdogs and y popcorn
∵ They buy a total of 11 hotdogs and popcorn
∵ The number of hotdogs is x and the number of popcorn is y
∴ x + y = 11 ⇒ (1)
∵ Hot dogs cost $2.50 each
∵ Popcorn costs $1.00 each
∵ They spend $20 on hot dogs and popcorn
→ Multiply x by 2.5 and y by 1, add the products and equate the sum by 20
∴ 2.5(x) + 1(y) = 20
∴ 2.5x + y = 20 ⇒ (2)
Now we have a system of equations to solve it
→ Subtract equation (1) from equation (2)
∵ (2.5x - x) + (y - y) = (20 - 11)
∴ 1.5x + 0 = 9
∴ 1.5x = 9
→ Divide both sides by 1.5 to find x
∴ x = 6
→ Substitute the value of x in equation (1) to find y
∵ 6 + y = 11
→ Subtract 6 from both sides
∴ 6 - 6 + y = 11 - 6
∴ y = 5
∴ They buy 6 hotdogs and 5 popcorn
Answer:
The next step is to combine constants
Step-by-step explanation:
X+y+z=22
(x+y+z+t)/4=8
subsitute
x+y+z=22
(22+t)/4=8
multiplly by 4
22+t=32
subtract 22
t=10
the fourth number is 10
Answer:
y = 4x + 3
Step-by-step explanation:
To do this, put the new line into the form y = mx + b where m is the slope and b is the y-intercept.
When two lines are parallel, they have the same slope. Since, the slope of the first line is 4, that means the slope of the second line is also 4.
So far, the equation is y = 4x + b.
Then, since you know (-2, -5) is a solution, x = -2, y = -5 is a solution so you can plug this into the equation.
This would be:
-5 = 4 * -2 + b
-5 = -8 + b
3 = b
This means the equation is y = 4x + 3.
Answer:
b and d
Step-by-step explanation:
