A sprout in Jessie's garden 26/5 cm tall and is growing 13/10 cm each week. Write and solve an equation in order to determine how many weeks it will take for the plant to be 13cm tall

6 weeks

Step-by-step explanation:

This one is pretty easy, and you could actually do logic here.

First, we know that the plant is initially 26/5 cm tall (5.2 cm), and each week grows 13/10 cm (1.3 cm). we have here two incognites, one is the number of weeks required and the other is the size of the sprout.

If we want to reach to 13 cm of tall, this is the final size of the sprout. To do this we know that the sprout grows every week a constant height, therefore, let Y be the size of the sprout and X the number of week.

Y = 13/10x

But the sprout is already with an innitial height of 26/5 cm, therefore, we need to start from there, and add that height into the equation:

Y = 26/5 + 13/10x or Y = 5.2 + 1.3x

Now, let's solve this equation to know the number of weeks needed to reach 13 cm.

13 = 5.2 + 1.3x

solving for x:

13 - 5.2 = 1.3x

x = 13 - 5.2 / 1.3

x = 6

So it will take 6 weeks for the sprout to reach 13 cm of tall