I have a number, 𝑥. I add three to my number. Then, I divide the answer by five. My final answer is 2.78. Calculate my final answer if, instead, I add five to my number, 𝑥, and then divide by three.
This is a two-step problem. Firstly, we need to work out the number 𝑥. Then, we need to calculate the final answer using the new operations. We were told in the first line that the number is 𝑥. The second line told us that we add three to the number. This is written as 𝑥 plus three. The third line tells us that we divide the answer by five. This can be written as 𝑥 plus three over or divided by five. The fourth line tells us that the final answer is 2.78. Therefore, 𝑥 plus three divided by five must be equal to 2.78.
Our first step is to rearrange this equation to calculate the value of 𝑥. We will do this using the balancing method. The opposite of dividing by five is multiplying by five. Therefore, our first step is to multiply both sides of the equation by five. Multiplying the left-hand side by five means that the fives cancel. This leaves us with 𝑥 plus three. On the right-hand side, we need to multiply 2.78 by five. Typing this into the calculator gives us an answer of 13.9.
Our next step is to subtract three from both sides of this equation as subtracting three is the opposite or inverse of adding three. Once again, on the left-hand side, the threes cancel. This leaves us with 𝑥. On the right-hand side, 13.9 minus three is equal to 10.9. Therefore, our value for 𝑥 is 10.9.
We can check this answer by substituting 10.9 back into the initial equation. We were told to add three to our number 𝑥 and then divide the answer by five. 10.9 plus three divided by five is equal to 2.78. Therefore, our value for 𝑥 is correct.
We now need to deal with the second part of the question. We need to calculate the final answer when we add five to 𝑥 and then divide by three. Adding five to 𝑥 would give us 𝑥 plus five. We then need to divide this answer by three. We know that our value for 𝑥 is 10.9. So we need to substitute this into the expression. This gives us 10.9 plus five divided by three. 10.9 plus five is equal to 15.9. Dividing this by three gives us 5.3.
The final answer when we add five to 𝑥 and then divide by three is 5.3.