Ezra and Leah took their families to the movie theater last weekend, and they each spent the same amount of money. Ezra bought 5 tickets and spent $12 on popcorn, while Leah bought 3 tickets and spent $24 on popcorn plus $9 on sodas.
Which equation can you use to find p, the price of each movie ticket?
What was the price of each movie ticket?
Let p be the price of each movie ticket. The total amount spent by Ezra and Leah can be represented by the following equation:
5p + 12 = 3p + 24 + 9
Solving for p:
2p + 12 = 33
2p = 21
p = 10.5
Therefore, the price of each movie ticket is $10.50.
In the summertime, Rick likes to buy cherries at the farmers market. On his first visit of the season, he bought 2
1
4
pounds of cherries. On his next visit, he bought 3
1
2
pounds of cherries and used a coupon to get $7 off his purchase. He noticed that he was charged the same amount each time.
Which equation can you use to find p, the price of a pound of cherries?
What is the price of a pound of cherries?
Let p be the price of a pound of cherries. The total amount that Rick spent on his first visit and the total amount he spent on his second visit can be represented by the following equation:
2.25p = 3.5p - 7
Solving for p:
3.5p - 2.25p = 7
1.25p = 7
p = 5.6
Therefore, the price of a pound of cherries is $5.60.
Beth and her cousin Albert both collect stamps. Beth currently has 80 stamps in her collection, and she adds 4 more each month. Right now, Albert only has 20 stamps in his collection, but he adds 10 more each month.
Which equation can you use to find m, the number of months it will take for Albert to have as many stamps as Beth?
How many months will it take for Albert to have as many stamps as Beth?
Let m be the number of months it will take for Albert to have as many stamps as Beth. The total number of stamps each person will have after m months can be represented by the following equation:
80 + 4m = 20 + 10m
Solving for m:
10m - 4m = 80 - 20
6m = 60
m = 10
Therefore, it will take Albert 10 months to have as many stamps as Beth.
Samir and Ben are planning a day trip with their friends. Samir wants to go to a waterpark that charges $40 per person for admission, plus $5 per person for tube rentals. Ben wants to go to a rock-climbing gym that charges $150 to rent the facility, plus an additional $20 per person.
Which equation can you use to find p, the number of people who would need to go on the trip for the two options to cost the same?
How many people would need to go on the trip for the two options to cost the same?
Let p be the number of people that need to go on the trip for the two options to cost the same. The total cost for each option can be represented by the following equations:
For Samir's option:
Cost = 40p + 5p
For Ben's option:
Cost = 150 + 20p
Setting the two equations equal to each other:
40p + 5p = 150 + 20p
Solving for p:
45p = 150 + 20p
25p = 150
p = 6
Therefore, 6 people would need to go on the trip for the two options to cost the same.
Scarlett and Tristan are both running for student council president. At the start of the last day of voting, Tristan had half as many votes as Scarlett. Throughout the day, Scarlett gained 11 more votes, while Tristan gained 34 more votes. By the end of the day, Scarlett and Tristan had the same number of votes.
How many votes did Scarlett have at the start of the last day of voting?
Let's denote the initial number of votes Scarlett had as S and the initial number of votes Tristan had as T. Given the information in the question, we can write the following equations:
1) T = 0.5S
2) S + 11 = T + 34
Substitute the value of T from equation 1 into equation 2:
S + 11 = 0.5S + 34
0.5S = 23
S = 46
Therefore, Scarlett had 46 votes at the start of the last day of voting.
Joy bought some granola from the bulk bins at the grocery store. Emilio bought one-third as much granola as Joy, but he also spent $4.41 on milk and $6.17 on fresh berries. Joy and Emilio ended up spending the same amount of money.
How much did Joy spend on granola?