Sally grew 18 flowers with 9 seed packets. How many seed packets does Sally need to have a total of 44 flowers in her garden? Assume the relationship is directly proportional.

22 seed packets

Step-by-step explanation:

we can look at this in a couple of ways. the first way to solve this is an algebraic problem. we know that 18 flowers came from 9 packets so 18 is going to be on one side of the equation while 9 is going to be on the other. we dont know how many seeds were in each packet though so we will use x to represent the amount of seeds. now our equation looks like this: 18 = 9x. heres how to solve it:

given: 18 = 9x

to get x alone we divide each side by 9 because its the opposite of muliplication: 2 = x

x = 2 seeds per packet

another way we could figure this out is by using proportions. when we see the ratio flowers to packet is 18:9, we can tell that it needs to be simplified. we know both 9 and 18 are divisible by 9 so when we do that we get the answer, our ratio of flowers to packets is 2:1.

next, we need to look back at how we solved that problem we just did, and plug in our new numbers. when doing it algebraically, we follow these steps:

plug in: 44 = (x)2

x times 2 is equal to 2x: 44 = 2x

to get x alone divide each side by 2 because its the opposite of multiplication: 22 = x

x = 22

if we want to solve it using ratios and proportionalities, we set it up flowers to packets like before so we have the ratio 44:x. seeing that the ratio was 2:1 last time, we know that 44 is 2 times x, or x is 1/2 (half) of 44. so we can find half of 44 to get x. half of 44 is 22 so 44:22 is the ratio's answer.

i hope this helped :))