Answer: Choice A) x = 15; y = 17
---------------------
Explanation:
The "7x+7" angle and the "112 degree" angle are congruent. They are vertical angles. So
7x+7 = 112
7x+7-7 = 112-7
7x = 105
7x/7 = 105/7
x = 15
We technically have enough to stop here, but let's keep going to find y
The "4y" angle and the "112 degree" angle are supplementary. They form a single straight line. They add to 180 degrees
So,
4y+112 = 180
4y+112-112 = 180-112
4y = 68
4y/4 = 68/4
y = 17
V=π*r^2*h
therefore the height must be:
h=V/(π*r^2)
Insert your values:
h=45π/(π*3^2)=5
The height is 5.
Let the number of $1.50 wrenches be x,
number of $2.50 wrenches = x
number of $4 wrenches = x/2
number of $3 wrenches = x/2 + 1
amount paid for $1.50 wrenches = 1.5x
amount paid for $2.50 wrenches = 2.5x
amount paid for $4 wrenches = 4(x/2)
= 2x
amount paid for $3 wrenches = 3(x/2 + 1)
= 1.5x + 3
total amount paid = 1.5x + 2.5x + 2x + 1.5x + 3
= 7.5x + 3
7.5x + 3 = 78
7.5x = 75
x = 10
number of $1.50 wrenches = x
= 10
number of $2.50 wrenches = x
= 10
number of $4 wrenches = x/2
= 10/2
= 5
number of $3 wrenches = x/2 + 1
= 10/2 + 1
= 5 + 1
= 6
He bought 10 $1.50 wrenches, 10 $2.50 wrenches, 5 $4 wrenches and 6 $3 wrenches.
45=5x+10
-10=5x-10
35=5x
X=7
