Solving Systems of Equations (Including Word Problems)
Suppose I sell 30 tickets to a high school, all children's and adult tickets. Each children's ticket is $5 and each adult ticket is $7. The total revenue from all tickets is $176. How many of each ticket was sold?
Children's Tickets Sold: 17
Adult Tickets Sold: 13
1/x-3 + 10/(x-3)^3 = 2x+3/(x-3)^2
-7 and 4
(x^4 - 8)/14 + 1 = 5
You can't have the positive root of a negative number so -48 = x^4 is an empty set. The answer is +/- 2(fourth root of 4)
5|2x + 3| + 18 = 8
-3/2 and -5/2 do not work when plugged into the equation so empty set.
4x-20(x-2) = x+3
37/17
Vir went to a donut shop to buy donuts for everyone in his math class. He bought 50 donuts in all, in three different flavors: chocolate, glazed, sprinkled. There was one more than twice as many glazed donuts as chocolate donuts. Chocolate donuts cost 40 cents per donut, glazed cost 30 per donut, and sprinkled cost 50 cents per donut. If the total cost of all donuts was $18.80, how many of each donut did he buy?
Chocolate Donuts Bought: 12
Glazed Donuts Bought: 25
Sprinkled Donuts Bought: 13
The Ryan Publishing Company has two printing presses. It takes the new printing press 45 min to print 10,000 fliers. Together the two presses can print the 10,000 fliers in 30 min. How long does it take the older printing press by itself to print the 10,000 fliers?
90 minutes / 1.5 hours
3x^2 + 5x + 1 = 0
-5 +/- √13
_________
6
|2(x-3)^2 − 9| + 4 = 20
x = 3 + (5√2)/2
x = 3 - (5√2)/2
5x-10(x+25) = 20x-10
x=-9.6 or -9 3/5
I want to make a 20-pound mixture made of granola, M&Ms, and peanuts that is worth $3.60 per pound. I also want to have twice as many pounds of M&Ms as granola, since I am a chocoholic. If peanuts are worth $3 per pound, M&Ms are worth $4 per pound, and granola is worth $5 per pound, how many pounds of each should I use?
Peanuts: 11 lbs
M&Ms: 6 lbs
Granola: 3 lbs
For exercise, Joseph likes to walk and Vincent likes to ride his bike. Vincent rides his bike 12 km/h faster than Joseph walks. Joseph walks 20 km in the same amount of time that Vincent rides 44 km. Find the rate that each of them travels.
Joseph: 10 km/h
Vincent: 22 km/h
3x^2 + 78 = 0
x^2 = -26
You can't square root a negative so empty set.
2 |3x + 4| – 3 > 15
When you plug in 5/3 and -13/3, you get 15 > 15, which isn't true, since there isn't an "or equal to" sign. Therefore, the answer is an empty set.
Write the slope-intercept equation of a line passing through (1,2) and (3,5).
y=3/2x+1/2
Solve for (x, y)
y=x^2-5x
2x+y=4
(x, y)=(4, -4) U (-1, 6)
Pedro can bike twice as fast as he can run. One day he biked 10 miles to his grandmother's house, and he ran back. The entire trip took 2.5 hours. How fast did Pedro run?
-11 + 24x^2 = 9 - 39x^2
x = +/- 60√7/63
8|x - 1|^4 + 6 = 10
1 +/- fourth root of 8/2
−7x − 12 + 5 − 13x + 1= 21
x=-3/4
We have two different salt solutions, A and B. If we mix 100g of each solution, the resulting solution is 10% salt. If we mix 400g of A and 600g of B, the solution is 9% salt. What percentage of salt is solutions A and B?
A= 15% salt
B= 5% salt
Three pipes are connected to a water tank. One of the pipes can fill the tank in 30 minutes. The second pipe can fill it in 20 minutes. The third pipe can fill the tank in 40 minutes. If the slowest pipe is shut off after 3 minutes and the fastest pipe is shut off 3 minutes later, how long will it take the remaining pipe to finish filling the tank?
12 min 45 seconds
16x^4 + 4x^2 = 0
x = 0 since you can't square root a negative and 0 was a possible value after setting 4x^2 equal to 0.
|3x + 4| ≤ x + 2
Interval Notation: [-3/2,-1]
Compound Inequality: -3/2 ≤ x ≤ -1
2x-(3x-1)/10=(3-x)/2
x=8/11