If a is a non-zero digit in the numbers 1a2a and
a31, what is the value of a when
1a2a + a31 = 2659?
To find the value of a, let's look at the given equation: 1a2a + a31 = 2659.
We know that a is a non-zero digit, which means it can be any digit from 1 to 9.
Let's break down the numbers:
1a2a can be written as 1000 + 100a + 20 + a.
So, 1a2a = 1000 + 100a + 20 + a = 1020 + 101a.
a31 can be written as 100a + 30 + 1.
So, a31 = 100a + 30 + 1 = 100a + 31.
Now, we can substitute the values into the equation:
1020 + 101a + 100a + 31 = 2659.
Simplifying the equation:
1020 + 101a + 100a + 31 = 2659.
105a + 1051 = 2659.
105a = 2659 - 1051.
105a = 1608.
To solve for a, we divide both sides by 105:
a = 1608 / 105.
a ≈ 15.31.
Since a must be a non-zero digit, the value of a cannot be 15.31. Hence, there is no valid value of a that satisfies the equation 1a2a + a31 = 2659.
To find the value of a, we can use algebraic equations.
Let's break down the given numbers:
1a2a = 1000 + 100a + 20 + a = 1001a + 20
a31 = 100 + 30 + a = 131 + a
Now, we can rewrite the equation:
(1001a + 20) + (131 + a) = 2659
Simplifying the equation:
1001a + 20 + 131 + a = 2659
1002a + 151 = 2659
1002a = 2659 - 151
1002a = 2508
To find the value of a, divide both sides of the equation by 1002:
a = 2508 / 1002
Using long division, we get:
a = 2
Therefore, the value of a is 2.
a+1 = 9 ????
1828 + 831 = ????