C B A are the orders of the answers
If Ava has 34 candy bars, and each box can hold 5 bars, then we need to find out how many boxes that are filled up.
Divide the number of candy bars (34), by the number each box can hold (5)
Since we cannot have 6.8 boxes, we have to round down to 6.
To check our answer, we multiply the number of boxes (6), by the number of bars in each box (5), to get 30. We add Ava's extra bars (4), and we get the number we started off with: 34. This proves our answer is correct!
Number of weekend minutes used: x
Number of weekday minutes used: y
This month Nick was billed for 643 minutes:
(1) x+y=643
The charge for these minutes was $35.44
Telephone company charges $0.04 per minute for weekend calls (x)
and $0.08 per minute for calls made on weekdays (y)
(2) 0.04x+0.08y=35.44
We have a system of 2 equations and 2 unkowns:
(1) x+y=643
(2) 0.04x+0.08y=35.44
Using the method of substitution
Isolating x from the first equation:
(1) x+y-y=643-y
(3) x=643-y
Replacing x by 643-y in the second equation
(2) 0.04x+0.08y=35.44
0.04(643-y)+0.08y=35.44
25.72-0.04y+0.08y=35.44
0.04y+25.72=35.44
Solving for y:
0.04y+25.72-25.72=35.44-25.72
0.04y=9.72
Dividing both sides of the equation by 0.04:
0.04y/0.04=9.72/0.04
y=243
Replacing y by 243 in the equation (3)
(3) x=643-y
x=643-243
x=400
Answers:
The number of weekends minutes used was 400
The number of weekdays minutes used was 243
Answer: First option 13
Solution
If ABCD is a rhombus, the diagonals must be perpendicular, then the angle (5x+25)° must be a right angle (90°):
(5x+25)°=90°
5x+25=90
Solving for x: Subtracting 25 both sides of the equation:
5x+25-25=90-25
Subtracting:
5x=65
Dividing both sides of the equation by 5:
5x/5=65/5
Dividing:
x=13
Answer: The value of x must be 13
