IN Harry's Backyard, his peach tree produces two pieces of fruit for every three pieces of fruit that grow on his apricot tree. If there is a total of 265 fruits between the two trees, how many pieces of fruit does each have?
2006-10-17 19:30:56 · 13 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
All we have to do to solve this is to set up a system of equations and then solve for each variable.
Let { x = amount of fruit produced by his peach tree
y = amount of fruit produced by his apricot tree
Our first equation can be y + x = 265, because we know that the total of the fruit produced is 265, so the sum of the fruits produced on each tree will be = to the total amount produced
Our second equation can be 2y = 3x, because "his peach tree produces two pieces of fruit for every three pieces of fruit that grow on his apricot tree"
So we have:
y + x = 265
2y = 3x
Lets substitute.
y + x = 265 --> x = 265 - y (plug in 265 - y for x in the second equation)
2y = 3(265 - y)
2y = 795 - 3y
5y = 795
y = 159
So we know that his apricot tree produced 159 pieces of fruit. Lets plug this back in to the original.
x = 265 - (159)
x = 106
So we know that his peach tree produced 106.
Lets check. is 106/159 the same as 2/3? If so, the proportion is correct. And it is.
Is 106 + 159 = 265? Again, yes.
This means that our results are correct! The total number of fruits produced by Harry's peach tree is 106, and the total number of fruit produced by Harry's apricot tree is 159!
Hope this helps!
2006-10-17 19:41:25 · answer #1 · answered by mattomynameo 4 · 1⤊ 0⤋
Let the no. fruits in the peach tree be 2x
therefore no. of fruits in apricot tree is 3x
So total no. of fruits is 2x+3x = 5x or 265 fruits
so , 5x = 265
or x = 265/5 = 53
so x = 53 , so 2x = 53x2=106 and 3x=53x3=159
so no. of peaches = 106
no. of apricots = 159
I would be glad if this helped you
2006-10-17 20:52:18 · answer #2 · answered by Aneesh 2 · 0⤊ 0⤋
You can use algebra to solve this problem. Let's assume that the peaches produced is P, and the apricots produced is A. Then, we can make one equation 2P=3A, since for every two peaches, there are 3 apricots. We can make one more equation: A+P=265.
Now, by using simultaneous equations (or substitution), we find out that A=106 and P=159.
2006-10-17 19:36:19 · answer #3 · answered by Gimmip 2 · 1⤊ 0⤋
Apricots:159
Peaches:106
2006-10-17 19:37:00 · answer #4 · answered by Ria L 2 · 0⤊ 0⤋
2P + 3A = 5 F
Divide by 5
2P/5 + 3A/5 = 1F
Multiply by 265:
2*265P/5 + 3*265A/5 = 265F
106 peaches + 159 apricots = 265 fruits
2006-10-17 19:42:23 · answer #5 · answered by Helmut 7 · 0⤊ 0⤋
Apricots:159
Peaches:106
simple
2006-10-17 21:39:48 · answer #6 · answered by Anonymous · 0⤊ 0⤋
2/5*265 and 3/5*265
=106 and 159
2006-10-17 20:07:15 · answer #7 · answered by raj 7 · 0⤊ 0⤋
106 peaches and 159 apricots
2006-10-17 19:42:40 · answer #8 · answered by nandu 1 · 0⤊ 0⤋
i may assist you with one. All of those are similar issues and a similar good judgment will word to all of them. a million. (a - 6) divided through 5 = 7/12 what's a? A-6 ------ = 7/12 5 Your purpose is to isolate A on the left aspect and all else on the right. First, get rid of the 5 through mutiplying each and every aspect through 5 A-6 = 5 * 7/12 A-6 = 35/12 Now, flow -6 (word the minus signal) to authentic of the equivalent signal A= 35/12 + 6 meaning A = 35/12 + seventy 2/12 = 107/12 A=107/12
2016-10-16 05:23:47 · answer #9 · answered by Anonymous · 0⤊ 0⤋
p = 2 * a/3
p+a=265
frojm these two equations follow a
2/3a = 265-a
5a=3*265 or a = 3*265/5
and p = 2*265/5
2006-10-17 19:34:33 · answer #10 · answered by gjmb1960 7 · 0⤊ 0⤋