Equations and Inequalities

The equation -0.45x + 14 = 12 - 0.35x represents the following situation:
Jenny lit a 12-inch candle and a 14-inch candle at the same time. The 14-inch candle melted at a rate of 0.45 inches per hour while the 12-inch candle melted at a rate of 0.35 inches per hour. How many hours, x, will it take for before the two candles will be the same height?

The solution is x = 20

What does x = 10 mean in the context of the situation above?

​

​ (a)  

What will the height of the candles be?

​ ​ (b)  

• 20 hours
• 20 inches
• 20 candles
• 20 days
• 5 inches
• 5 seconds
• 5 candles
• 5 days

WRITE AN EQUATION TO REPRESENT THE SITUATION

Celebrity A has 400 followers on social media and is gaining 75 followers each day. Celebrity B has 1,000 followers on social media, but is losing 25 followers a day.

• 400 - 75x = 1,000 + 25x

• 400 + 75x = 1,000 – 25x

• 400x - 75 = 1,000x + 25

• 400x + 75 = 1,000x – 25

SOLVE THE EQUATION

Celebrity A has 400 followers on social media and is gaining 75 followers each day. Celebrity B has 1,000 followers on social media, but is losing 25 followers a day. How many days will it take them to have the same number of followers?

• 4 days

• 5 days

• 6 days

• 7 days

WRITE AN EQUATION TO REPRESENT THE SITUATION

Peter and his friends are going to play putt-putt. At one location, they can pay $2.00 for rentals plus $7.50 per game. At another location, it would cost $8.00 for rentals plus $6.00 per game.

• 2 + 7.50x = 8 + 6x

• 2 - 7.50x = 8 - 6x

• 2x + 7.50 = 8x + 6

• 2x - 7.50x = 8 x- 6

SOLVE THE EQUATION

Peter and his friends are going to play putt-putt. At one location, they can pay $2.00 for rentals plus $7.50 per game. At another location, it would cost $8.00 for rentals plus $6.00 per game. How many games would they have to play in order for either location to cost the same amount?

• 2 games

• 3 games

• 4 games

• 5 games

WRITE AN EQUATION TO REPRESENT THE SITUATION

Shelby has $155 in savings, and her boyfriend George has $230. Shelby is saving $10 each week, and George is spending $15 each week.

• 155x - 10 = 230x + 15

• 155x + 10 = 230x – 15

• 155 - 10x = 230 + 15x

• 155 + 10x = 230 – 15x

SOLVE THE EQUATION

Shelby has $155 in savings, and her boyfriend George has $230. Shelby is saving $10 each week, and George is spending $15 each week. After how many weeks will their savings accounts have the same amount of money in them?

• 8 weeks

• 7 weeks

• 4 weeks

• 3 weeks

Renting games online from Netwii costs $3.33 per game  with no monthly fee.  Renting games online from HDO costs $2.00 per game plus a monthly fee of $10.00.
Which inequality represents the situation when the monthly cost at Netwii is more than the monthly cost at HDO?

• 3.33v > 2v + 10
• 3.33v + 10 > 2v 
• 3.33v < 2v + 10
• 3.33v + 10 < 2v

Yellow Cab Taxi charges a $1.75 flat rate in addition to $0.65 per mile.  Katie has no more than $10 to spend on the taxi ride.

• 1.75 + 0.65m < 10
• 1.75 + 0.65m > 10
• 1.75m + 0.65 < 10
• 1.75m + 0.65 > 10

Renting games online from Netwii costs $3.33 per game  with no monthly fee.  Renting games online from HDO costs $2.00 per game plus a monthly fee of $10.00.
Which inequality represents the situation when the monthly cost at Netwii is more than the monthly cost at HDO?

• 3.33v > 2v + 10
• 3.33v + 10 > 2v 
• 3.33v < 2v + 10
• 3.33v + 10 < 2v