Avery's office recycled a total of 14 kilograms of paper over 7 weeks. After 9 weeks, how many kilograms of paper will Avery's office have recycled? Assume the relationship is directly proportional.

Question

i need help

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Answer 1

Hello!

There are a few ways you can solve this type of problem:

#1. You can use proportions.

To do this, set up 2 fractions that are equal to each other. (X is the unknown that we are solving for).

14 kg = x

7 weeks 9 weeks

Next we need to cross-multiply. (Multiply the numerator of the first proportion by the denominator of the second proportion, and multiply the denominator of the first proportion by the numerator of the second proportion. Set these equal to each other).

14 × 9 = 7 × x (Solve for x)

126 = 7x

7 7 (Divide both sides by 7 to get x by itself)

18 = x

#2.You can figure out how many kg are recycled each week, and then determine how many for 9 weeks.

First we will divide 14 kg by 7 weeks because we know that the office recycles this amount in 7 weeks.

14 ÷ 7 = 2 kg recycled in 1 week.

Next we will multiply the kg of paper recycled in 1 week by 9 (because we want to know how much is recycled in 9 weeks).

2 kg × 9 weeks = 18 kg recycled in 9 weeks.

I hope this was helpful! Please reach out if you have any questions!

Holly Anderson

Answer 2

Hello, Maggie,

It isn't as bad as it might first appear. We just have to accept that the phrase "directly proportional" means that Avery's office recycled at the same rate the entire period. Let's find out that rate, in kg/week. 14 kg was recycled in 7 weeks, so the office recycles at a rate of 2 kg/week.

We could phrase this in an equation by stating the amount of paper recycled (P) is equal to the number of weeks (W) time 2 kg/week:

P = W*2 kg/week

At W = 7, they recycled 14 kg

At W = 9, they would have recycled (9 weeks)*(2 kg/week) = 18 kg

We could have calculated a rate in units of kg/day or even kg/min, but the question used units of weeks, so that's what I used.

Bob

Answer 3

y =kx

14 = k7

k=2

After 9 weeks

9*2= 18