the difference of two numbers is 10. the sum of three times the smaller number and four times the larger is 75. find the numbers

Answer 1

so lets represent the numbers as variables
x will be the bigger number and y smaller.
x-y=10 3y+4x=75
solve for x
x-y=10 x=10+y
plug x into the other equation
3y+4(10+y)=75 3y+40+4y=75
solve for y and then plug it back into the equation to solve for x.