Question

If a+1=b+2=c+3=d+4=a+b+c+d+5, then (a+b+c+d) is equal to​

Answer 1

Answer:

First, I'll write the question in a better way:

a+1 = b+2 = c+3 = d+4 = a+b+c+d+5.

There are various ways to solve this, but let's solve it using the substitution method. What is that?

The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation.

If I write all the terms (b,c, and d) in terms of a, then I would be able to add or subtract them, right?

Here,

a+1 = b+2

b = a-1 ------------- (1)

a+1 = c+3

c = a-2 -----------(2)

a+1 = d+4

d = a-3 ----------(3)

Now, we know, a+1 = a+b+c+d+5

Now let's substitute the values of b,c, and d as in terms of 'a'.

a+1 = a+(a-1)+(a-2)+(a-3)+5

a+1 = a+a+a+a-1-2-3+5

a+1 = 4a-6+5

a+1 = 4a-1

a-4a = -2

-3a = -2

a = $\frac{2}{3}$

But our Aim is to find (a+b+c+d). We know, a+b+c+d+5 = a + 1

So,

a+b+c+d = a + 1 - 5

a+b+c+d= a-4

a+b+c+d = $\frac{2}{3}$ - 4

a+b+c+d = $\frac{2}{3} - \frac{12}{3}$

a+b+c+d = $\frac{-10}{3}$.

If you have a doubt on whether these values are wrong, don't worry, I have checked them by hand, and I got correct results whilst substitution of their corresponding numerical values.

Hope it Helps,

Byeeee