Mr. Adams said that 10 more than 7 times his age is 9 years fewer than 5 times his age with the digits reversed. How old is Mr. Adams?
59
Heather, your answer does not work
10 more than 7 times 59 = 423
9 fewer than 5 times his age reversed
= 5(95) - 9 = 466
let the tens digit of his age be x
let the units digit of his age be y
his age is 10x+y
10 more than 7 times his age
= 7(10x+y) + 10
9 fewer than 5 times his age with the digits reversed
= 5(10y+x) - 9
they are equal:
7(10x+y) + 10 = 5(10y+x) - 9
70x + 7y + 10 = 50y + 5x - 9
65x - 43y = -19
65x = 43y - 19
if y = 8
65x = 43(8)-19 = 325
x = 5
so Mr Adams is 58
check:
10 more than 7 times his age = 7(58)+10 = 416
9 less than 5 times age reversed = 5(85) - 9 = 416
all is good!
To find the age of Mr. Adams, let's break down the given information and solve the equation step-by-step.
First, let's represent Mr. Adams' age as a variable, say "x".
According to the statement, "10 more than 7 times his age," we can write the expression as "7x + 10".
Similarly, "9 years fewer than 5 times his age with the digits reversed" can be written as "5x - 9", where we reverse the digits from 59 to 95.
Now we can set up the equation based on the given information:
7x + 10 = 5x - 9
To solve this equation, first, we need to simplify it by combining like terms:
7x - 5x = -9 - 10
2x = -19
Divide both sides of the equation by 2:
2x/2 = -19/2
This simplifies to:
x = -19/2
Since the age cannot be negative, Mr. Adams' age is not a fraction and cannot be -19/2.
Therefore, there is no real solution for Mr. Adams' age based on the given information.