Rafael is making punch and needs a gallon of raspberry sorbet and 2 liters of Sprite to make 12 cups. He pays $3.00 for a 2-liter container of Sprite and $4.00 for a quart of sorbet. What is the minimum amount he should charge per cup of punch to make a $10 profit? (Remember there are 4 quarts in a gallon.) Your answer should be a dollar amount rounded to the nearest hundredth.
To make 12 cups of punch, Rafael needs a gallon of raspberry sorbet, which is 4 quarts, or 16 cups. He also needs 2 liters of Sprite, which is approximately 8.45 cups.
The cost of the sorbet is $4.00 per quart, so the cost of a gallon (4 quarts) of sorbet is 4 * $4.00 = $16.00.
The cost of the Sprite is $3.00 for a 2-liter container, which is approximately 8.45 cups. So the cost of 2 liters of Sprite is $3.00.
Therefore, the total cost of the ingredients is $16.00 + $3.00 = $19.00.
To make a $10.00 profit, Rafael needs to charge at least $19.00 + $10.00 = $29.00 for the punch.
Since he's making 12 cups, Rafael should charge at least $29.00 / 12 cups = $2.42 per cup.
Therefore, he should charge at least $2.42 per cup to make a $10 profit.
Randi needs to mow her lawn. The mixture requires 5 gallons of gas for every 2 gallons of oil. How much oil will she need for 8 gallons of gas?
To determine the amount of oil needed for 8 gallons of gas in a 5:2 ratio, we can set up a proportion.
The ratio of gas to oil is 5:2, which can be represented as 5/2.
Let x be the amount of oil needed for 8 gallons of gas.
Therefore, the equation becomes:
5/2 = 8/x
Cross-multiplying:
5x = 2 * 8
5x = 16
Dividing both sides by 5:
x = 16/5
x = 3.2
Therefore, Randi will need 3.2 gallons of oil for 8 gallons of gas.
Use proportional relationships to solve this mixture problem. The incoming 6th-grade class has a choice between band or choir as an elective. There are four times as many seats in choir as there are in band. How many students can choose band if there are a total of 250 students?
Let's represent the number of seats in band as "b" and the number of seats in choir as "c".
According to the problem, the ratio of the number of seats in choir to band is 4:1. This can be written as:
c/b = 4/1
We can also determine the total number of seats available by adding the number of seats in band and choir:
b + c = total number of seats
According to the problem, there are a total of 250 students, so we can substitute this value into our equation:
b + c = 250
We will use these two equations to find the value of "b".
To solve the system of equations, we can isolate "c" in terms of "b" from the first equation:
c = (4/1) * b
c = 4b
Substitute this expression for "c" in the second equation:
b + 4b = 250
5b = 250
b = 250/5
b = 50
Therefore, there are 50 students who can choose band as their elective.
Carla has to complete her science homework. She has 20 pages to read and 14 questions to answer. If it takes Carla 10 minutes to read 4 pages, How many minutes will it take her to read the full assignment?
Carla takes 10 minutes to read 4 pages. Let's set up a proportion to find the time it will take her to read the entire assignment.
10 minutes / 4 pages = x minutes / 20 pages
Cross-multiplying:
4x = 10 * 20
4x = 200
Dividing both sides by 4:
x = 200 / 4
x = 50
Therefore, it will take Carla 50 minutes to read the full assignment.
Luis is making chocolate chip cookies. The recipe calls for 1/8 cup of almonds for every 3/4 cup of chocolate chips. If Luis uses 3 cups of chocolate chips, how many cups of almonds will he need?
To determine the number of cups of almonds Luis will need when using 3 cups of chocolate chips, we can set up a proportion.
The ratio of almonds to chocolate chips is 1/8 cup : 3/4 cup.
Let x be the number of cups of almonds needed.
Therefore, the equation becomes:
(x cups) / (3/4 cups) = 1/8 cups
To solve this proportion, we will cross-multiply:
(x cups) * (8/1 cups) = (3/4 cups) * (1/1 cups)
8x = 3/4
To find x, we divide both sides by 8:
x = (3/4) / 8
To divide a fraction by a whole number, we multiply the numerator by the reciprocal of the denominator. Therefore:
x = (3/4) * (1/8)
Multiplying the numerators and denominators:
x = 3/32
Therefore, Luis will need 3/32 cups of almonds when using 3 cups of chocolate chips.