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:
1st fraction =
2/6*3/2
2nd fraction =
3/6*2/2
Step-by-step explanation:
Let the required number be x, then
x + 3,080 = 5,082
x = 5,082 - 3,080
x = 2,002
First blank: sin. C = h/a
The ratio for sin. is opposite (the height) over hypotenuse (a).
Second blank: Area = (1/2)b(a sin. C)
In this substitution, we are substituting the value of h into the traditional area of a triangle formula.
Third Blank: Area = (1/2)ab(sin C)
We are using the commutative property to move the position of a.
Hope this helps and good luck in your classes!
