Child's homework puzzle is baffling adults

Can you solve this number pyramid puzzle?

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[JonSebastianF]

*Alternative approach*
The whole pyramid can be written simply as:
40 = (7 + ★) + (★ + 9)
And then you take it from there.

[daindreska]

It's not a particularly difficult problem, but I definitely didn't expect to see it being given at such a young age.

[edmx]

To be fair, most adults are baffled by splitting a restaurant bill.

[xyzct]

At a coffee shop my bill was $5.25.
I gave the barista a $10 bill and a quarter.
It was like watching the Hindenburg 2.0

[llaffer]

The way I did this was notice that the way the pyramid was built, if we call the 3 numbers on the bottom x, y, and z, the number shown at the top is (x + 2y + z). I could then use that to solve for star immediately. Once we know that, we can solve for heart by adding the 9, then add the two together. I got 33.

[MrGhosta]

The hardest part was figuring out what the question was actually asking me to do.

At first I thought it was asking me to solve a ratio but then realized it's just a really badly written substitution problem.

Math used to be straight forward and would just ask you to solve for X: 40 = (7+X) + (9+X). Now we have to decipher what the question is even asking us to do.

[CharlesBallowe]

My first instinct was "40 = blank box + heart" and "blank box = 7 + star" so ... "40 = 7 + star + heart" and then "33 = star + heart" which is the answer. Apparently this was the "clever" answer.

[ogi]

To be fair, that REALLY is a difficult problem for a 9yo. It requires figuring out a way to solve a problem by substitution.

[NerdByAnyOtherName]

My logic was that 7 and 9 are two apart, and both 7 and 9 are being added to the same number to create the middle numbers and therefore the middle numbers must also be two apart, and the only way to do that to get 40 is 19+21 so the middle row is 19|21 and the rest of the puzzle solves itself from there.

[Xeroph-]

As my old maths teacher said: "A lot of things are just quadratic equations in disguise."

[davidreid]

Simply 40-7-9= 2 x star. So star= 12 . Rest follows.

[craigstephens]

My initial approach was that the numbers in the middle row must be 2 apart (9 - 7). That means the blank must be 19 and the heart 21 in order to get 40. Then star is 12 and the solution is 33.

[coreywest]

The way I did it was the 2 numbers that add to 40 must have a 2 digit difference (because of 7 and 9) therefor must be 19 and 21. The rest is pretty straight forward

[Maninawig]

Adult: I never used algebra in real life!
Kids: it shows.

[TravisGn]

I just used the fact that blank = 7 + star, to get to 7 + star + heart = 40.

Meaning that star + heart = 33

I didn't bother working out the individual values at first but when I did I just used the 7 and the 9 to know that the heart and blank have a range of 2, meaning that they are 21 and 19 respectively. Then it's pretty simple to work out that the star is 12

[yorelyoung]

The total is 40. This means that you need to figure out what number can be added to 7 and 9 to make two numbers that equal 40.

7+12= 19
9+12=21
19+21=40
And this is based on the rules established at the start before his explanation.

[verkuilb]

I used a different method: I noticed immediately that the triangle is Pascal’s Triangle—so the top sum is equal to the bottom left plus the bottom right plus double the bottom center. That immediately solved the star to be 12. The heart is then 12+9.

The Pascal’s Triangle method works even if additional rows were added to the bottom of the triangle.

[ErikBongers]

As others also noted, but I like to phrase it differently:
All values come from the bottom and simply trickle up. However the middle value trickles up twice!
So 40 is the sum of the bottom values, with the middle value added twice. This quickly gives you a middle value of 12.

[collingallaway]

I think I solved this is a pretty simple way: since we know that the middle number is the sum of the 2 numbers below it, I noticed that the top number would be the sum of of the outer numbers on the bottom row + 2 times the middle number. In reverse you just subtract the 2 outer numbers from the top (40-7-9) to get 24 which is 2*12. Thus the bottom middle number is 12 and can be used to calculate the remaining values

[angeldude]

Each cell is the sum of the two below it. So 7 + x = y, 9 + x = z, y + z = 40. We only need to know x + z, so sub (1) into (3) for 7 + x + z = 40 and subtract 7 from both sides for x + z = 33. We don't even need to know what x or z are.