How Many Solutions?
How many solutions does this equation have? If one, what is the solution?
0=4
Zero
Solve the equation for x.
5x = 4x + 2
x = 2
Solve for x.
A + x = B
x = B - A
A student earned money tutoring during the summer. She charged $15 per session and also received a $30 bonus from her school. Altogether, she earned $180.
What is the equation of this scenario?
15x + 30 = 180
You have $40 in your savings account, and your friend has $70. You deposit $10 per week, and your friend deposits $5 per week. In how many weeks will you both have the same amount of money?
Write an equation and solve.
40 + 10x = 70 + 5x
x = 6
How many solutions does this equation have? If one, what is the solution?
4x = 4x
Infinite
Solve the equation for a.
6a + 3 = 3(a + 4)
a = 3
Solve for w.
A = l * w
w = A/l
A food truck owner made money selling tacos at a school event. He earned $6 for each taco sold. After paying a $24 permit fee, he had $120 left.
What is the equation of this scenario?
6x - 24 = 120
Two candles are burning. Candle A starts at 30 cm tall and melts at a rate of 2 cm per hour. Candle B starts at 50 cm tall and melts at a rate of 4 cm per hour. After how many hours will the candles be the same height?
30 - 2x = 50 - 4x
x = 10
How many solutions does this equation have? If one, what is the solution?
1/2(8x + 40) = 10x + 2
One.
x = 3
Solve the equation for y.
−4y+9=1+5y−y
y = -1
Solve for h.
P = 2(h + w)
h = (P - 2w)/2
A student sold handmade bracelets for a school fundraiser. Each bracelet sold for $5, and every customer also donated an extra $3. Altogether, the student raised $96.
What is the equation of this scenario?
A phone battery starts at 100% and drains at 5% per hour. Another phone starts at 20% and charges at 10% per hour. After how many hours will both phones have the same battery percentage?
80 - 5x = 20 + 10x
x = 4
For what value of k will the following equation have infinitely many solutions?
k(2x + 5) = 12x + 30
k = 6
Solve the equation for x.
3(2x + 4) = -2(x - 4)
x = -1/2
Solve for p.
M = P/X
P = XM
A concert promoter pays $15 for each ticket. He also pays $2.00 in fees to list each ticket online. The promoter pays a one-time advertising fee of $120. In total, he paid $970.
What is the equation that represents this story?
How many tickets did the promoter buy?
15x + 2x + 120 = 970 OR 17x + 120 = 970
He bought 50 tickets.
A hiking trail has two groups. Group A starts at 11 miles up the mountain and hikes down at a rate 1.5 miles per hour. Group B starts at 2 miles up the mountain and continues hiking upwards at 0.5 miles per hour. After how many hours will both groups have traveled the same total distance?
12 - 1.5x = 2 + 0.5x
x = 5
For what value of k will the following equation have infinitely many solutions?
-3(2x - 2)= 1/4kx + 6
k = -24
Solve for x.
1/3 ( 6 x − 18 ) = 3( x + 4 )
x = -18
Solve for b.
L = F/B + 2
B = F/(l - 2)
A school club orders custom T-shirts for a fundraiser. Each T-shirt costs $18 to make, and there is an additional $4 printing fee for each shirt. The club also pays a one-time setup fee of $140. In total, the club spent $1,130.
What is the equation that represents this story?
How many shirts did the club make?
18x + 4x + 140 = 1,130 or 22x + 140 = 1,130
They made 45 shirts.
A parking garage tracks available spaces. Garage A starts with 300 empty spaces and loses 12.5 spaces per hour as cars arrive. Garage B starts with 150 empty spaces and gains 7.5 spaces per hour as cars leave. After how many hours will both garages have the same number of empty spaces?
300 - 12.5x = 150 + 7.5x
x = 7.5