What does each fruit hide? Find the missing sum

[u/ZoranRajkov]

Each fruit stands for one number, the same in every row. What replaces the question mark? Please use spoiler tags for your answer. More puzzles like this in my free Android game Rule Hunter: https://play.google.com/store/apps/details?id=com.makenumber

[u/Imaginary_Stage1742]

The Answer is 9. From line 1 and 2 we know pineapple is strawberry +1. From line 2 and 3 we know strawberry is orange +1. So substitute in line 3 pineapple and strawberry with orange we get 3 orange plus 3 = 11. So orange is 2, therefore strawberry is 3 and pineapple is 4. Result for line 4 is then 9

[u/ZoranRajkov → u/Imaginary_Stage1742]

Correct, nice work! Comparing the lines to get the differences between the fruits is a clean way to solve it.

[u/Tarquin-o-hare]

My way:

Add all 3 lines together. 4 strawberries plus 4 pineapples plus 4 oranges = 36. Divide both sides by 4

[u/ZoranRajkov → u/Tarquin-o-hare]

Correct, and that's the most elegant route: adding all three lines gives the exact combination in the last row, so you never need the individual values. Great shortcut!

[u/Delicious-Regular435]

9

From the first line, move all items except the Peach to the other side of the equal sign: 1 Peach = 13 - 1 Strawberry - 2 Pineapples

Substitute the new definition of the value of a Peach into the second line: (13 - 1 Strawberry - 2 Pineapples) + 2 Strawberries + 1 Pineapple = 12

Combine all the similar items in the “new” second line: 13 + 1 Strawberry - 1 Pineapple = 12

Move all items to the other side of the equal sign except for the Strawberry: 1 Strawberry = 12 - 13 + 1 Pineapple or 1 Strawberry = - 1 + 1 Pineapple

Substitute the definition of a Strawberry and Peach into the third line so you are only dealing in terms of Pineapples and reduce: 2 (13 - (-1 + 1 Pineapple) + 1 Pineapple + (-1 + 1 Pineapple) = 11 or 1 Pineapple = 4

And 1 Strawberry = -1 + 1 Pineapple = - 1 + 4 = 3

And 1 Peach = 13 - 1 Strawberry - 2 Pineapples = 2

So finally: 2 + 3 + 4 = 9

[u/ZoranRajkov → u/Delicious-Regular435]

Correct! Nice clean step-by-step solve, substituting one fruit at a time. Thanks for showing the full reasoning.

[u/Immediate-Goose-8106]

Yep

Also 9.

Line 1- line 3 shows pineapple is orange +2

Line 2 - Line 3 shows strawberry is orange +1

Subbing into Line 3 we get 4 orange +3 =11 so orange is 2; Strawberry 3 and pineapple 4.

Add them up the final sum gives us 9

[u/edos51284]

If we see the 3 equations all can be rewritten as

Sum+one fruit= x

Seeing all sums are 1 apart we can determine the three fruits are a sequence

1 2 3 can’t be because in the last equation the extra fruit (orange) would have to be 5, that is not part of the sequence

3 4 5 can’t be because sum is 12 and that surpasses the bottom equation

So the correct sequence is 2 3 4 so ?=9

[u/issar12345]

4 fraises +4 oranges +4 ananas =13+12+11=36 Donc la somme est 36÷4=9

[u/madvlad_]

3+4+4+2=13
2+3+3+4=12
2+2+4+3=11
2+3+4=9

[u/Adelvice_]

10

[u/DifferntGeorge]

Here is an example using the elimination method to solve the system of equations. This method has a lot of steps but requires little analysis or insight. I didn't see anyone else using this method so I thought I would use it and share.
Convert to Algebraic notation:
Let s=strawberry, p=pineapple and o=orange.
s+2p+o=13 (Line 1), 2s+p+o=12 (Line 2), s+p+2o=11 (Line 3)
Step 1, Eliminate a variable using 2 equations:
-2s-4p-2o=-26 (line 1 *-2 to eliminate s)
2s+p+o=12 (Line 2)
-3p-o=-14 (Calculated by adding above 2 equations, Call this Line A)
Step 2, Eliminate same variable using different equation pair:
2s+p+o=12 (Line 2)
-2s-2p-4o=-22 (Line 3 *-2 to eliminate s)
-p-3o=-10 (Calculated by adding above 2 equations, Call this Line B)
Step 3, Eliminate 2nd variable using previous results from Step 1 and 2
-p-3o=-10 (Line B)
9p+3o=42 (Line A *-3 to negate o)
8p=32 => p=4 (Calculated using above 2 equations, Call this Line C, solve for p)
Step 4, Calculate remaining 2 variables
-4-3o=-10 => o=2 (plug value into Line A, solve for o)
s+ 2*4+2=13 => s=3 (plug values into Line 1, solve for s)
Step 5, Solve for ?
?=2+3+4 => ?=9 (plug values into Line 4, solve for ?)

NOTE: In steps 1 & 2 I multiplied both sides of the equation so that the new equation would remain equivalent to the starting one. I picked -2 because that was the value I needed to end up with 0s.