SOLUTION: The number 66 is divided into smaller numbers. One number is 3 more than twice the other number. Find the larger of the two numbers.

Question 75804: The number 66 is divided into smaller numbers. One number is 3 more than twice the other number. Find the larger of the two numbers.
Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
From the information in the problem we can write two equations. The first equation
comes from the fact that one number (call it x) and another number (call it y) add
up to be 66. So the first of our equations is:
.
x + y = 66
.
The second equation comes from the information that x is 3 more than twice y. In equation
form this can be written as:
.
x = 2y + 3
.
Substitute this into the first equation by replacing x by 2y + 3 and the first equation
becomes:
.
2y + 3 + y = 66
.
Subtract 3 from both sides for the purpose of eliminating the + 3 from the left side. When
you do this subtraction the equation becomes:
.
2y + y = 63
.
Add the terms on the left side and you get:
.
3y = 63
.
Divide both sides by 3 to find that:
.
y = 63/3 = 21
.
Since x + y = 66 we can substitute 21 for y to find that x + 21 = 66. Subtracting
21 from both sides we find that x = 66 - 21 = 45. So the larger of the two numbers
is 45.
.
Hope this helps you to understand that two equations can be used to solve this problem
and gives you some insight into the substitution method of solving the set of two equations.
RELATED QUESTIONS
The number 66 is divided into smaller numbers. One number is 3 more than twice the other... (answered by stanbon)

Sum of two numbers is 66.the larger number is three more than twice the smaller number.... (answered by Cromlix)

One number is four more than the other. The square of the smaller number increased by... (answered by stanbon)

One number is ten more than other. If the sum of twice the smaller number and three times (answered by josmiceli)

The sum of two numbers is 66. The larger number is three more than twice the smaller... (answered by checkley79)

One number is twice the other number. The larger of the two numbers is 25 more than 1/3th (answered by mananth)

Twice the smaller of two numbers is one-half of the larger number. The larger is 10 more... (answered by fractalier)

one number is three more than another number. the quotient of the larger number divided... (answered by ankor@dixie-net.com)

One number is 12 more than the other. The sum of the smaller number and twice the larger... (answered by checkley77,Mathtut)