SOLUTION: The sum of two numbers is 21.five times the first number added to 2 times the second number is 66.find the numbers

Question 1210391: The sum of two numbers is 21.five times the first number added to 2 times the second number is 66.find the numbers
Found 6 solutions by Edwin McCravy, MathLover1, timofer, ikleyn, mccravyedwin, greenestamps:
Answer by Edwin McCravy(20054)   (Show Source): You can put this solution on YOUR website!

The sum of two numbers, x = first number y = second number is 21. So x + y = 21 five times the first number added to 2 times the second number is 66. 5x + 2y = 66 Solve the first equation for y: y = 21 - x. Substitute in the second equation: 5x + 2(21 - x) = 66 5x + 42 - 2x = 66 3x = 66 - 42 3x = 24 x = 8 y = 21 - (8) y = 13 Answer: The first number is 8 and the second number is 13. Yes, I know it can be done with only one unknown. But I think it's much easier when students can think of each single number mentioned in the word problem as represented by one single letter, than it is to have to think of the second number as the complicated combination of a number, a sign, and an expression in the letter used for the first number. Edwin

Answer by MathLover1(20849)   (Show Source): You can put this solution on YOUR website!

let’s the numbers be and
if the sum of two numbers is , we have
.......solve for
...........eq.1
if five times the first number added to times the second number is . we have
.......solve for

............eq.2

from eq.1 and eq.2 we have
.........both sides multiply by

go to
...........eq.1, substitute

so. your numbers are and

Answer by timofer(104)   (Show Source): You can put this solution on YOUR website!
if one of them is x
other is 21-x.

Solve that equation.

--------------One of the numbers. Easily identify the other number.
Answer by ikleyn(52776)   (Show Source): You can put this solution on YOUR website!
.
The sum of two numbers is 21. Five times the first number added to 2 times the second number is 66. Find the numbers.
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

        I will show here how to solve this problem MENTALLY, without using equations.

It is clear that we can re-formulate the problem this way: Two times the first number added to 2 times the second number is 42. Five times the first number added to 2 times the second number is 66. Find the numbers Looking in these two lines, your brain may conclude that three times (3 = 5-2) the first number is the difference 66-42 = 24. Hence, first number is 24/3 = 8. Then the second number is 21-8 = 13. ANSWER. First number is 8. Second number is 13.

Solved MENTALLY, without using equations.

Answer by mccravyedwin(406)   (Show Source): You can put this solution on YOUR website!

We should not tutor on here as if the students who post here are gifted students. The truth is that the majority of students who come on here are STRUGGLING!!! Edwin

Answer by greenestamps(13198)   (Show Source): You can put this solution on YOUR website!

Some of the tutors who have responded use a single variable to solve the problem. Others use two variables to make two equations and then use substitution to solve the problem.

Those are valid methods. But with the problem worded the way it is, forming two equations in two unknowns and solving by elimination would seem to be the most direct approach.

x = first number
y = second number

(1) x+y = 21 (the sum of the two numbers is 21)

(2) 5x+2y = 66 (5 times the first number plus 2 times the second is 66)

Multiply (1) by 2:
(3) 2x+2y = 42

Find the difference between (2) and (3) to eliminate y: 3x=24

Solve: x = 8

Substitute x = 8 into (1) to find y:
8+y = 21
y = 13

Note that this solution is exactly equivalent to the good "mental" solution provided by another of the tutors.

ANSWERS: 8 and 13

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