George weeded 1/5 of the garden and Summer weeded some too. When they were done 2/3 was left of the garden. How much did Summer weed.

Step-by-step explanation:

Step one) Figure our what peace of information you need to find and write down what information you already know.

•George weeded 1/5 of the garden.

•At the end 2/3 of the garden was left, which means that 1/3 of the garden was weeded.

•Now we need to figure out how much Summer weeded.

Step Two) Find the LCM (Lowest common multiple) of 5 and 3.

The LCM of 5 and 3 is 15.

Step three) Change the denominator of both problems to 15. Now the information you have should be:

•George weeded 3/15 of the garden. (We get the 3 on top because we multiplied 5 x 3 to get 15 so we multiply the numerator by 3 as well.)

•At the end there was 10/15 left. (We get the ten on top because the bottom was multiplied 3 x 5 to get 15, so then we take the numerator which is 2 and multiply that by 5 as well.)

•Now we know that if 10/15 weren’t picked that means that 5/15 were picked.

•We still need to figure out the amount that was picked by Summer.

Step 4)

Now we will use all the previous information to do the final step.

If a total of 5/15 were picked, and 3/15 of those were picked by George, then we do the problem:

5-3=2

Sally picked 2/15.

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4