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Example Questions
Example Question #31 : Linear / Rational / Variable Equations
What is the slope of the line 7y – 4x = 27
Adding 4x to both sides of the equation and dividing by 7 yields a slope of 4/7.
Example Question #1801 : Act Math
If you drove at an average speed of 78 miles per hour, what distance, in miles, did you drive in 140 minutes?
1.8
182
4,680
156
182
140 minutes is 7/3 of an hour. Multiplied by the speed of 78mph, we obtain 182 miles traveled.
Example Question #1802 : Act Math
3x + 9i2 – 5x = 17
What is x?
13
4
–13
–1
–4
–13
i =
i2 = -1
3x + 9i2 – 5x = 17
3x + 9(–1) – 5x = 17
–2x – 9 = 17
–2x = 26
x = –13
Example Question #32 : Linear / Rational / Variable Equations
Solve for x:
3x + 4y = 26
–5x + 12y = 14
Eliminate y and solve for x.
3x + 4y = 26 (multiply by –3)
–5x + 12y = 14
(–3)3x +(–3) 4y = (–3)26
–5x + 12y = 14
–9x +-12y = –78
–5x + 12y = 14
–14x + 0y = –64
x = –64/–14 = 32/7
Example Question #1801 : Act Math
Michael is counting his money. He notices he has one more quarter than he does dimes, as well as one less nickel than dimes. The total cash he has is $2.60. How many coins does he have in total?
The general form for money problems is
, where
is the value of the coin and
is the number of coins.
Let = # of dimes,
= # of quarters, and
= # of nickels.
So, , and solving gives
. Therefore there are 6 dimes, 7 quarters, and 5 nickels, giving 18 coins in total.
Example Question #33 : Linear / Rational / Variable Equations
What value of will satisfy the equation
The answer is .
The solve this equation, first distribute the to obtain
Proceed to subtract from both sides to get
Subtract from both sides to leave
Divide both sides by to get the answer,
Example Question #1803 : Act Math
Given that , what is the value of
?
First, we must solve the equation for by subtracting
from both sides:
Then we must add to both sides:
Example Question #1806 : Sat Mathematics
Internet service costs $0.50 per minute for the first ten minutes and is $0.20 a minute thereafter. What is the equation that represents the cost of internet in dollars when time is greater than 10 minutes?
The first ten minutes will cost $5. From there we need to apply a $0.20 per-minute charge for every minute after ten. This gives
.
Example Question #1807 : Sat Mathematics
John goes on a trip of kilometers at a speed of
kilometers an hour. How long did the trip take?
If we take the units and look at division, will yield hours as a unit. Therefore the answer is
.
Example Question #1808 : Sat Mathematics
With a head wind a plane can fly a certain distance in five hours. The return flight takes an hour less. How fast was the plane flying?
In general, .
The distance is the same going and coming; however, the head wind affects the rate. The equation thus becomes .
Solving for gives
.
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