Question

Fill the Boxes
How fast can you fill the boxes?
14
= 10
II II
15 16
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Answer 1

$\left|\begin{array}{ccccc}\cline{1-5}\boxed{}&+&\boxed{}&=&14\\+&&+&&\\ \boxed{}&-&\boxed{}&=&10\\=&&=&&\\15&&16&&\\ \cline{1-5}\end{array}\right|$

Now we write the above system as follows:

$\left|\begin{array}{ccccc}\cline{1-5}\boxed{a}&+&\boxed{b}&=&14\\+&&+&&\\ \boxed{c}&-&\boxed{d}&=&10\\=&&=&&\\15&&16&&\\ \cline{1-5}\end{array}\right|$

So we can form four equations:

• a + b = 14 .....(i)
• a + c = 15 .....(ii)
• b + d = 16 .....(iii)
• c - d = 10 .....(iv)

(iii) + (iv) >>

b + d + c - d = 16 + 10

or, b + c = 26

or, c = 26 - b .....(v)

Putting c = 26 - b in (ii), we get

a + 26 - b = 15

or, a - b = - 11 .....(vi)

(i) + (vi) >>

a + b + a - b = 14 - 11

or, 2a = 3

or, a = 1.5

Putting a = 1.5 in (i), we get

1.5 + b = 14

or, b = 14 - 1.5

or, b = 12.5

Putting b = 12.5 in (v), we get

c = 26 - 12.5

or, c = 13.5

Putting c = 13.5 in (iv), we get

13.5 - d = 10

or, d = 13.5 - 10

or, d = 3.5

Thus we get:

$\left|\begin{array}{ccccc}\cline{1-5}\boxed{1.5}&+&\boxed{12.5}&=&14\\+&&+&&\\ \boxed{13.5}&-&\boxed{3.5}&=&10\\=&&=&&\\15&&16&&\\ \cline{1-5}\end{array}\right|$