Question 1119563: The difference between two numbers is 46. Four times the smaller is equal to 2 more than the larger. What are the numbers?
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! x is the smaller number.
y is the larger number.
x - y = 46
4 * y = x + 2
rearrange the terms so that all the variables are on the left side of the equation and the constants are on the right side of the equation and the variables are in consistent positions on the left.
you will get:
x - y = 46
-x + 4y = 2
add the second equation to the first to get:
3y = 48.
solve for y to get:
y = 48 / 3 = 16.
from the first equation of x - y = 46, replace y with 16 to get:
x - 16 = 46.
solve for x to get:
x = 62.
you have:
x = 62
y = 16
from the first equation, x - y = 46 becomes 62 - 16 = 46 which becomes 46 = 46 which is true.
from the second original equation, 4y = x + 2 becomes 4 * 16 = 62 + 2 which becomes 64 = 64 which is true.
both original equations are true when you replace x with 62 and y with 16.
your solution is that the larger number is equal to 62 and the smaller number is equal to 16.
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