+0

# HW help

+1
193
8
+1681

I think the answer is 2. If it is wrong, can you tell me why? And I used guesswork, so is there a more efficient way? And can you help me out by using that more efficient way and telling me how below?

Thank you

- tommarvoloriddle

Jul 1, 2019
edited by tommarvoloriddle  Jul 1, 2019

#1
+105466
+2

We can write

144

____   =     10   + a       multiply both sides by a

a

144  = 10a  + a^2       rearrange as

a^2 + 10a  - 144  = 0

We need two integers that sum to  10   and multiply to  -144

These are  18  and - 8

So

(a + 18) (a - 8)  = 0

Set each factor to 0  and solve for a

a + 18  = 0                                     a - 8  = 0

a  = -18   (reject)                             a = 8     (this is the solution)

Jul 1, 2019
#4
+1681
+10

Thank you CPHILL

tommarvoloriddle  Jul 1, 2019
#5
+105466
0

Welcome.....

CPhill  Jul 1, 2019
#6
+1681
+10

:)

-tommarvoloriddle

tommarvoloriddle  Jul 1, 2019
#7
+2505
+2

You thought $$\Delta$$ could be a two digit number, and assumed it was 12.

However, in the problem, it states "1$$\Delta$$". It cannot be "112"

So in the future, be careful, remember that when "1$$\Delta$$" happens, $$\Delta$$ must be SINGLE digit number.

CalculatorUser  Jul 2, 2019
#8
+1681
+5

:) whooooops

tommarvoloriddle  Jul 2, 2019
#2
+106080
+2

Did you test 2?

144/2=72   there is not a 1 in the units column so it cannot be correct.

You could just try all the possible answers, there are only 9 of them, 1 through 9 but better still, do it as I have below

$$let \;\;x=\triangle$$

$$\frac{144}{x}=10+x\\ 144=x^2+10x\\ x^2+10x-144=0\\ x=\frac{-10\pm\sqrt{100+576}}{2}\\ x=\frac{-10\pm\sqrt{676}}{2}\\ x=\frac{-10\pm26}{2}\\ x=-5\pm13\\ x = -18\;\;or\;\;8$$

but x is a 1 digit number so it is 8

$$\triangle \;\;is\;\;8$$

check:   144/8=18     there is a one in the tens column and an 8 in the units so it works.

.
Jul 1, 2019
edited by Melody  Jul 1, 2019
#3
+1681
+11

Whoops. Thank you Melody!

tommarvoloriddle  Jul 1, 2019