The sum of a number and 19 divided by two is five more than three times the number. Write an equation to represent the statement above. Let 𝑥 represent the number.
As we are letting 𝑥 represent the number, then the sum of a number and 19 can be written as 𝑥 plus 19. We then need to divide this by two. So we have 𝑥 plus 19 divided by two. We were told that this is five more than three times the number. Three times the number is equal to three 𝑥 and five more than this is three 𝑥 plus five. These two expressions are equal to each other.
This means that the equation that represents the statement is 𝑥 plus 19 divided by two is equal to three 𝑥 plus five. Whilst we weren’t explicitly asked to in this question, we can solve this equation to calculate the value of the number 𝑥. Multiplying both sides of the equation by two gives us 𝑥 plus 19 is equal to two multiplied by three 𝑥 plus five.
Expanding the bracket or parenthesis gives us six 𝑥 plus 10 as two multiplied by three 𝑥 is equal to six 𝑥 and two multiplied by five is equal to 10. Subtracting 𝑥 from both sides of this equation gives us 19 is equal to five 𝑥 plus 10. We can then subtract 10 from both sides of the equation. This leaves us with nine is equal to five 𝑥 or five 𝑥 equals nine. Finally, dividing both sides by five gives us a value of 𝑥 of nine-fifths or nine over five.
Nine-fifths is equivalent to one and four-fifths or 1.8. We can, therefore, see that the value for 𝑥 was equal to 1.8.
We can substitute this value into the left- and right-hand side of the equation and check that they are equal to each other. 1.8 plus 19 is equal to 20.8 and 20.8 divided by two is equal to 10.4. Therefore, the left-hand side is equal to 10.4. Substituting 𝑥 equals 1.8 into the right-hand side gives us three multiplied by 1.8 plus five. Three multiplied by 1.8 is equal to 5.4. And adding five to this also gives us 10.4.
We have, therefore, proved that the correct equation was 𝑥 plus 19 divided by two is equal to three 𝑥 plus five. And our value for 𝑥 would be 1.8 or nine-fifths.