SOLUTION: A number consists of two digits with a sum of 7 .If the number is increased by 3 it is equal to 11 times the tens digit. Find the number

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Question 1066389: A number consists of two digits with a sum of 7 .If the number is increased by 3 it is equal to 11 times the tens digit. Find the number
Answer by Theo(13342) (Show Source):
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let a equal the tens digit.

let b equal the ones digit.

the sum of the digits is equal to 7.

you get a + b = 7.

the number itself is unknown.

let x equal the number.

that gets you 10 * a + b = x

if the number is increased by 3 it is equal to 11 times the tens digit.

that gets you x + 3 = 11 * a.

since 10 * a + b = x, replace x with 10 * a + b to get 10 * a + b + 3 = 11 * a.

solve for a to get a = b + 3.

since a + b = 7, replace a with b + 3 to get b + 3 + b = 7.

solve for b to get b = 2

since a + b = 7, then a must be equal to 5.

your number has to be 52.

add 3 to it and you get 55.

55 / 5 is equal to 11.

solution looks good.