a third of a number is equal to the half of another number, if you add these two numbers together you get a sum of 30. What are these two numbers, show work please!
Let first number is = x
Let 2nd number is = y
a third of a number= x / 3
a half of 2nd number= y / 2
a third of a number is equal to the half of another number
x / 3 = y / 2
2x = 3y
or
x=3y/2
if you add these two numbers together you get a sum of 30
x / 3 + y / 2 =30
Multiply with 6
2x + 3y = 180
Put
2.3y/2 + 3y =180
3y+3y=180
6y=180
y=30
Put y=30 in Put
x=30*3 / 2
x=45
1/3x = 1/2y
x + y = 30
x = 30 - y
Substitute:
(1/3) * (30 - y) = 1/2y
10 - 1/3y = 1/2y
Multiply both sides by 6
60 - 2y = 3y
60 = 5y
y = 12
x + 12 = 30
x = 18
*Don't forget to check work:
1/3 * 18 = 6
1/2 * 12 = 6
5 and 25
Comments
Let first number is = x
Let 2nd number is = y
a third of a number= x / 3
a half of 2nd number= y / 2
a third of a number is equal to the half of another number
x / 3 = y / 2
2x = 3y
or
x=3y/2
if you add these two numbers together you get a sum of 30
x / 3 + y / 2 =30
Multiply with 6
2x + 3y = 180
Put
x=3y/2
2.3y/2 + 3y =180
3y+3y=180
6y=180
y=30
Put y=30 in Put
x=3y/2
x=30*3 / 2
x=45
1/3x = 1/2y
x + y = 30
x = 30 - y
Substitute:
(1/3) * (30 - y) = 1/2y
10 - 1/3y = 1/2y
Multiply both sides by 6
60 - 2y = 3y
60 = 5y
y = 12
x + 12 = 30
x = 18
*Don't forget to check work:
1/3 * 18 = 6
1/2 * 12 = 6
5 and 25