word problem - fruit

[fifty]

Jon had an equal number of apples and pears. He gave away 66 pears. He then had 4 times as many apples as pears. How many fruits did he begin with?

my approach:

A = P

P = P - 66
A = 4P

4p = p-66
3p = -66
p=-22

66+22 = 88
4 x 22 = 88

176 frutis.

Problem is, I have a -22 and that mucks up the answer. Where did I mess up?

 

[stapel]

Jon had an equal number of apples and pears. He gave away 66 pears. He then had 4 times as many apples as pears. How many fruits did he begin with?

my approach:

A = P

P = P - 66

The last line above means "0 = -66", which obviously isn't true. So let's start over, clearly labelling as we go, so our meaning is clear.

original quantities:
. . .pears: P
. . .apples: P

...because the number of apples is equal to the number of pears, so there's no need for a second variable. Then:

new quantities:
. . .pears: P - 66
. . .apples: 4(P - 66)

The number of apples didn't change, and you now have two expressions for the number of apples. Set those expressions equal, and solve. Back-solve to find the requested information.

 

[HallsofIvy]

Jon had an equal number of apples and pears. He gave away 66 pears. He then had 4 times as many apples as pears. How many fruits did he begin with?

my approach:

A = P

Your first mistake is not explicitely stating what "A" and "P" stand for, at least for yourself. Jon started with an equal number of apples and pears so "A= P" if "A" is the number of apples he started with and "P" the number of pears he started with.

P = P - 66

And this is the result of not being clear what "P" stands for! He started with "P" pears. After giving away some, he no longer has "P" pears. You might have noticed that if you subtract "P" from both sides of this equation, you are left with "0= -66" which definitely is NOT true!

If you called "the number of pears he had after giving 55 away" P', then P'= P- 66

A = 4P

So this would be A= 4P' or simply A= 4(P- 66).

Since, initially A= P this is the same as P= 4(P- 66)= 4P- 264.

Subtract P from both sides and add 264 to both sides: 264= 3P so P= 264/3= 88.

4p = p-66
3p = -66
p=-22

66+22 = 88
4 x 22 = 88

176 frutis.

Problem is, I have a -22 and that mucks up the answer. Where did I mess up?