Amber's birthday party will cost $12 if she invites 4 guests. If there are 7 guests, how much will Amber's birthday party cost (c)? Assume the relationship is directly proportional.
We can set up a proportion to solve for c:
4 guests = $12
7 guests = c
We can find the constant of proportionality by dividing the cost by the number of guests:
12/4 = 3
Now we can use this constant to find the cost for 7 guests:
7 * 3 = 21
Therefore, Amber's birthday party will cost $21 if she invites 7 guests.
Chris jogged 1/3
of a mile to his friends house in 1/12
of an hour. Compute the unit rate of miles per hour.
To compute the unit rate of miles per hour, we need to divide the distance (in miles) by the time (in hours).
Chris jogged 1/3 of a mile in 1/12 of an hour, so:
Unit rate = distance / time
Unit rate = (1/3 mile) / (1/12 hour)
To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction:
Unit rate = (1/3 mile) * (12/1 hour)
Unit rate = 4 miles/hour
Therefore, the unit rate of Chris's jog is 4 miles per hour.
Mark's dog ran 3/4
of a mile in 1/4
of an hour. Compute the unit rate of miles per hour.
To compute the unit rate of miles per hour, we need to divide the distance (in miles) by the time (in hours).
Mark's dog ran 3/4 of a mile in 1/4 of an hour, so:
Unit rate = distance / time
Unit rate = (3/4 mile) / (1/4 hour)
To divide fractions, we can multiply the first fraction by the reciprocal of the second fraction:
Unit rate = (3/4 mile) * (4/1 hour)
Unit rate = 3 miles/hour
Therefore, the unit rate of Mark's dog's run is 3 miles per hour.
It takes 1/3
cups of powered punch mix to make 2/3
gallons of punch. If the recipe is for 1 gallon of punch, how much punch mix is needed to make 1/4
the recipe?
We can start by finding out how much punch mix is needed to make 1 gallon of punch. If it takes 1/3 cup of punch mix to make 2/3 gallons of punch, then we can set up a proportion:
1/3 cups / 2/3 gallons = x cups / 1 gallon
To solve for x, we can cross-multiply and simplify:
2/3 * x cups = 1/3 cups
x = 1/3 cups / 2/3
x = 1/2 cups
So it takes 1/2 cup of punch mix to make 1 gallon of punch.
To find out how much punch mix is needed to make 1/4 of the recipe (or 1/4 gallon of punch), we can use a proportion again:
1/2 cups / 1 gallon = x cups / 1/4 gallon
To solve for x, we can cross-multiply and simplify:
1/2 * 1/4 cups = x
x = 1/8 cups
Therefore, it takes 1/8 cup of punch mix to make 1/4 of the recipe or 1/4 gallon of punch.