Question

a*c*ac=ccc find value of a and c​

Answer 1

✰ Question :- if a * c * ac = ccc . Find the value of a and c .

✪ Solution :--

we know that,

☛ Any two digit number with unit digit as c and ten's digit as a can be written in the form = (10a + c)

Similarly,

☛ Any three digit number with all digit as c will be written

as = (100c + 10c + c ) .

Putting both in Question now, ( in place of ac we will put (10a+c) and ccc as 100c+10c+c ,,

➺ a * c * (10a + c) = 100c + 10c + c

➺ ac * (10a + c) = 111c

Dividing both sides by c , we get,

➺ a * (10a + c) = 111 ---------- Equation (1)

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Now, if we will do Prime Factorization of 111 , we can see ,

➼ 111 = 3 * 37

or,

➼ 111 = 3 * (3*10 + 7) -------- Equation (2)

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when we compare Equation (1) and Equation (2) now,

➳ a * (10a + c) = 3 * (3*10 + 7)

we can see that,

☛ a = 3

☛ c = 7

Hence, value of a is 3 and c is 7.

( ✫ Nice Question ).

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Answer 2

Answer:

Value of a is 3 and c is 7

Step-by-step explanation:

We Have :-

a * c * ac = ccc

To Find :-

Value of a and c​

Solution :-

Lets take RHS first

ccc

we can write it as as one's , ten's , hunderd's place

( 100c + 10c + c ) ------------- ( i )

Now taking LHS

a * c * ac

we can also write it as as one's , ten's place

a * c * ( 10a + c ) -------------- ( ii )

Now taking ( i ) and ( ii ) together

a * c * ( 10a + c ) = ( 100c + 10c + c)

Taking c common from both sides

a * ( 10a + c ) = ( 100 + 10 + 1 )

a * ( 10a + c ) = 111

a * ( 10a + c ) = 3 * 37

a = 3 , ( 10a + c ) = 37

10 ( 3 ) + c = 37

c = 37 - 30

c = 7

Value of a is 3 and c is 7