Question

S

The sum of two numbers is 90. The larger
number is 14 more than 3 times the smaller
number. Find the numbers.
First complete the equations below. where x stands for
the larger number and y stands for the smaller numben
x+y = [?]; x =[]+[ ]y
Enter

Answer 1

x=71 and y=19

Explanation:

First, we write out the first sentence as an equation. This is x+y=90. We also know that x=3y+14 because of the second sentence. Using this, we can substitute x in the first equation with what it is (3y+14). This makes the new equation 3y+14+y=90. Then, we collect like terms by adding the 'y's together - making 4y+14=90. We need to make the letters on one side and the numbers on the other. To do this, we subtract 14 from each side, making 4y=76. We want to find out what 'y' is by itself (not multiplied by four) so we divide each side by 4. This means that we have found out that y=19 because 76÷4=19. Now, it is time to solve x. Using our new knowledge that y=19, we can replace y in the equation x+y=90 with 19 so now we have x+19=90. This is the same as 90-19=x and we know that 90-19=71, so x must be 71. In conclusion, x=71 and y=19.

I hope this helps, have a great day!