Ellie's class is having a holiday party, and she is in charge of bringing juice. She decides to bring powdered juice mix and add water to it at school. There is a proportional relationship between the volume of water Ellie uses to make the juice (in liters), x, and the number of scoops of juice mix she uses, y.
The equation that models this relationship is y=3x.
How many scoops of juice mix should Ellie combine with 6 liters of water? Write your answer as a whole number or decimal.
To find the number of scoops of juice mix, we can plug in the given volume of 6 liters for x in the equation y=3x.
y = 3 * 6
y = 18
Ellie should combine 18 scoops of juice mix with 6 liters of water.
Judy wants to save up some money to buy a new smartphone, so she babysits on the weekends. There is a proportional relationship between the time Judy spends babysitting (in hours), x, and the amount of money she earns babysitting (in dollars), y.
For 1 hour of babysitting, Judy earns $5. Write the equation for the relationship between x and y.
y=
To write the equation for the relationship between x and y, we can use the given information that Judy earns $5 for 1 hour of babysitting. Since there is a proportional relationship, we can write the equation as follows:
y = 5x
In this equation, x represents the number of hours Judy spends babysitting, and y represents the amount of money she earns babysitting in dollars.
Judy wants to save up some money to buy a new smartphone, so she babysits on the weekends. There is a proportional relationship between the time Judy spends babysitting (in hours), x, and the amount of money she earns babysitting (in dollars), y.
The equation that models this relationship is y=5x.
How much does Judy earn babysitting for 2 hours? Write your answer as a whole number or decimal.
To find out how much Judy earns babysitting for 2 hours, we can plug in 2 for x in the equation y=5x.
y = 5 * 2
y = 10
Judy earns $10 babysitting for 2 hours.
Judy wants to save up some money to buy a new smartphone, so she babysits on the weekends. There is a proportional relationship between the time Judy spends babysitting (in hours), x, and the amount of money she earns babysitting (in dollars), y.
The equation that models this relationship is y=5x.
How long does Judy need to babysit to earn $20? Write your answer as a whole number or decimal.
hours
To find out how long Judy needs to babysit to earn $20, we can set up the equation y=5x and replace y with 20:
20=5x
To solve for x, we divide both sides of the equation by 5:
20/5 = x
4 = x
Judy needs to babysit for 4 hours to earn $20.
Aubrey's favorite book is about Johnny Appleseed, the American pioneer who planted apple trees all across the country. Inspired by the story, Aubrey plants an apple seed in her backyard and tends the seed as it slowly grows into a tree. There is a proportional relationship between the age of Aubrey's apple tree (in years), x, and the height of the tree (in feet), y.
When Aubrey's apple tree is 30 years old, it is 18 feet tall. Write the equation for the relationship between x and y.
To write the equation for the relationship between x and y, we can use the given information that Aubrey's apple tree is 18 feet tall when it is 30 years old. Since there is a proportional relationship, we can write the equation as follows:
y = kx
where k is the constant of proportionality. To find the value of k, we can use the information that when the tree is 30 years old, it is 18 feet tall. Substituting these values into the equation, we get:
18 = k * 30
To solve for k, we divide both sides of the equation by 30:
k = 18/30
k = 6/10
k = 0.6
The equation for the relationship between the age of Aubrey's apple tree (in years), x, and the height of the tree (in feet), y is:
y = 0.6x
Aubrey's favorite book is about Johnny Appleseed, the American pioneer who planted apple trees all across the country. Inspired by the story, Aubrey plants an apple seed in her backyard and tends the seed as it slowly grows into a tree. There is a proportional relationship between the age of Aubrey's apple tree (in years), x, and the height of the tree (in feet), y.
The equation that models this relationship is y=0.6x.
If this rate continues, how old will Aubrey's apple tree be when it is 21 feet tall? Write your answer as a whole number or decimal.
years