### Home > MC1 > Chapter 9 > Lesson 9.2.5 > Problem9-106

9-106.

Five pounds of fertilizer is needed for $1000$ square feet of garden. To calculate how much fertilizer should be used for a $450$ square foot garden Alex wrote this proportion: $\frac { 5 \text{ lbs} } { 1000 \text{ ft} ^ { 2 } } = \frac { n \text{ lbs} } { 450 } \text{ ft} ^ { 2 }$.

1. Solve this proportion for n.

To solve this proportion, it would be useful to use cross multiplication. With this strategy you should multiply each side of the equation above by the denominators of each fraction. Then set the sides equal to each other and solve for $n$.

Using cross multiplication, your expression should look something like this: $5$ lbs. $\left(450 \text{ ft}^{2}\right) = 1000 \text{ ft}^{2} \left(n \text{ lbs.}\right)$
Can you multiply the left side and then find the value of $n$?

2. Solve the following problem using a similar proportion.
Juan makes four out of every nine shots he takes in basketball. At the same rate, how many shots will he make if he shoots 135 times?

If Juan makes four of nine shots, this is a ratio of $\frac{4}{9}$.

Your goal is to change this ratio to a ratio over 135. Can you make a proportion now?

Your proportion might look something like this: $\frac{4}{9}=\frac{x}{135}$.

Can you solve the proportion? Refer to the Math Notes box below if you are having trouble.

Juan will make $60$ shots if he shoots $135$ times. Did you remember to show your work?