(1 x 100)
(2 x 10)
(7 x 1)
(9 x 0.1)
By hypothesis, the price of the shoes is represented by x, and the price of the hat is represented by y.
"Devin spent a total of $64 dollars for shoes and a hat" can be represented by the equation x + y = 64
"The shoes cost $6 more than the hat" can be represented by the equation x=y+6
We can now create a system:
x + y = 64 (1)
x = y + 6 (2)
Let's use the value of x from equation 2 and replace in equation (1):
x + y = 64
y + 6 + y = 64
2y + 6 = 64
Subtract 6 from each side to have the variables on a side and the numbers on the other:
2y + 6 = 64
2y + 6 - 6 = 64 - 6
2y = 58
Then divide both sides by 2 to have the variable y alone on the first side and its value on the other side:
(2y)/2 = 58/2
y = 29
We found the value of y.
Now let's use the value of y in equation (1), in order to find the value of x:
x = y + 6
x = 29 + 6
x = 35
We found the value of x.
So the price of the shoes is x = $35 and the price of the hat is y = $29.
You can recheck your answer (very important):
x + y = 29 + 35 = 64 (David spent a total of $64 dollars for shoes and a hat)
y + 6 = 29 + 6 = 35 = x (The shoes cost $6 more than the hat)
Hope this Helps! :)
Answer:
Step-by-step explanation:
Common ratio r = a₂/a₁ = 16/(-4) = -4
a₄ = a₃(-4) = 256
a₅ = a₄(-4) = -1024
a₆ = a₅(-4) = 4096
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
Answer:
A
Step-by-step explanation:
