Problema Solution
one number is eight more than a second number. Three times the first is 2 less than 4 times the second. what are the numbers
Answer provided by our tutors
Write your two equations from the information given:
n = the first number and y = the second number
Here are the two equations we need to solve to find our mystery numbers:
n = 8 + y
3n = 4y - 2
Think of it this way: We know what n equals, so substitute it in the second equation so that we only have to solve for y.
3(8 + y) = 4y - 2
We have to multiply 3 times each number in the parenthesis:
24 + 3y = 4y - 2
Now put like terms on opposite sides of the = sign. Remember to switch signs as they cross over...
24 + 2 = 4y - 3y Now combine and solve for y...
26 = y
Now put y into the first equation to solve for n...
n = 8 + y
n = 8 + 26
n = 34
Now work the second equation...
3(34) = 4(26) - 2
102 = 104 - 2
102 = 102 bingo!
So we know that our two numbers fit the criteria...
34 is 8 more than 26
and 3 times 34 is 2 less than 4 times 26