Question

The difference between two numbers is 4. Three times the larger is 2 more than five times the smaller. Find the numbers.

Answer 1

da numbers are x and y

lets say x>y
differebec between x and y is 4
x-y=4


3 times the larger is 2 more than 5 times the smaller
3 times x is 2 more than 5 times y
3x=2+5y

ok so we gots
x-y=4 and
3x=2+5y

hmm
in the first one we can solve for x and subsitute
x-y=4
add y to both sides
x=y+4
subsitute y+4 for x

3x=2+5y
3(y+4)=2+5y
distribute
3y+12=2+5y
minus 3y both sides
12=2+2y
minus 2 both sides
10=2y
divide 2 both sides
5=y

subsitute back

x=y+4
x=5+4
x=9

the numbers are 9 and 5

Answer 2

Let x represent the larger number.
Let y represent the smaller number.
x-y=4 Given
3x=5y-2 Given
Now we can just substitute; let x=4+y
Substitute 4+y for x in the second equation:
3(4+y)=5y-2
12+3y=5y-2
-2y=-14
y=7
Substitute back (into BOTH equations to double check work).
x, the larger number, is 11