Find out the correct number to replace the question mark.
Source: Beijing Aidi International School summer test (2018-08-21). Author: 坦途国际教育
You are correct. The answer is 9.
The first line has 3 bears with hats totaling 21. So a bear with a hat is 21/3 = 7.
The next line is 2 sets of a bear in a bus plus a bear in a hat totaling 19. So we know a bear in a bus is (19-7)/2 = 6.
Next is a hat, a bear in a bus, and a bear in a hat totaling 15. So we know a hat is 15-6-7=2.
Now that we know a hat is 2, a bear must be 5 (7-2). If a bear is 5, than a bus is 1 (6-5)
A hat is 2, a bear is 5, and a bus is 1. That makes the last line 5 + 4*1 which does equal 9.
Adding neater formatting but here is solution:
The key to this puzzle is attention to detail about what each image truly is
For the first line:
We have 3 bears and 3 hats. This adds up to 21 meaning a bear + a hat = 7.
Next we have to look at the third line:
In this line we have a bear with a hat (7), a hat and a bus with a bear. In total then we have a bus of unknown value and 2 bears with hats valued at 7 each. To get the total sum of 15 an empty bus must equal 1 (15-(2x7)).
Back to the second line now:
There are 2 buses with a hat-less bear and one bear with a hat (7). Since each bus is worth 1 and the bear with hat is worth 7, subtracting 9 from 19 leaves 10 for the value of two bears and 5 for the value of each individual bear.
Value of a hat:
Since a hat and a bear is 7 and a bear is 5, a hat is worth 2.
To recap: A bear without hat is 5, two hats will be 4 and a bus is 1. 1x4 (BEDMAS/PEDMAS) is still 4. All that is left is 4 + 5 which equals 9.
Let t be the number of teddy bears, h hats and b buses. Then the equations are:
and we want to know:
Gaussian elimination tells us the answer is:
$t=5, h=2, b=1$, therefore $t+2hb=9$.
but there is a quick way:
From (1) $t+h=7$. From (3) $b=1$. From (2) and (3), $t-h=3 \implies t=5, h=2$.