A gift basket has a ratio of 3 pears to every4 apples. How many pears are there in a gift basket with 36 apples?
1 answer:
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Hello,
We know that if we make the same operation on both sides, we don't affect the equation:
For example:
Do you see? we add 2 on both sides and we don't affect the equality
We can do the same with the multiplication, for example
4=4 (i'll multiply both sides by 1/2)
Now, we do exactly the same in your excercise:
![P=2(L+W) \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,[multiply\,\,by\,\,1/2] \\ \\ P*\bold{ \frac{1}{2}}=2(L+W)*\bold{ \frac{1}{2}} \\ \\ \frac{P}{2}=L+W\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,[Subtract\,\,L]\\ \\ \frac{P}{2}-\bold{L}=L+W-\bold{L}\\ \\ \frac{P}{2}-\bold{L}=L-\bold{L}+W \\ \\ \frac{P}{2}-L=W\\ \\ \boxed{ W= \frac{P}{2}-L }](https://tex.z-dn.net/?f=P%3D2%28L%2BW%29%20%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5Bmultiply%5C%2C%5C%2Cby%5C%2C%5C%2C1%2F2%5D%20%5C%5C%20%5C%5C%20P%2A%5Cbold%7B%20%5Cfrac%7B1%7D%7B2%7D%7D%3D2%28L%2BW%29%2A%5Cbold%7B%20%5Cfrac%7B1%7D%7B2%7D%7D%20%5C%5C%20%20%5C%5C%20%5Cfrac%7BP%7D%7B2%7D%3DL%2BW%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5C%2C%5BSubtract%5C%2C%5C%2CL%5D%5C%5C%20%20%5C%5C%20%5Cfrac%7BP%7D%7B2%7D-%5Cbold%7BL%7D%3DL%2BW-%5Cbold%7BL%7D%5C%5C%20%20%5C%5C%20%5Cfrac%7BP%7D%7B2%7D-%5Cbold%7BL%7D%3DL-%5Cbold%7BL%7D%2BW%20%5C%5C%20%20%5C%5C%20%5Cfrac%7BP%7D%7B2%7D-L%3DW%5C%5C%20%5C%5C%20%5Cboxed%7B%20W%3D%20%5Cfrac%7BP%7D%7B2%7D-L%20%7D)
We know that if we make the same operation on both sides, we don't affect the equation:
For example:
Do you see? we add 2 on both sides and we don't affect the equality
We can do the same with the multiplication, for example
4=4 (i'll multiply both sides by 1/2)
Now, we do exactly the same in your excercise:
We want to cut pieces of length:
from 35 metal rods each 40in long, and we want to know how many we can cut.
In order to answer the question, we must compute the number of pieces that we can cut from each metal rod, and then multiply the result by the number of metal rods. Let's do that!
1) From each metal rod we can cut:
2) We have 35 metal rods, so the total number of pieces of 6 1/4 in that we can cut is:
Answer
We can cut 210 pieces from the 35 metal rods.
Remark: we see that by cutting the pieces we will have a waste of metal from each rod.