sum of two number is 119623807 . If one of them is 23349618 find the other number ? these is word problem question
Answers
Answer:
Sum of two numbers =119623807
One of them =23349618
Other=(119623807-23349618)=96274189
Step-by-step explanation:
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Answer:
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Table of Contents | Home
10
WORD PROBLEMS
Examples
Problems
WORD PROBLEMS require practice in translating verbal language into algebraic language. See Lesson 1, Problem 8. Yet, word problems fall into distinct types. Below are some examples.
Example 1. ax ± b = c. All problems like the following lead eventually to an equation in that simple form.
Jane spent $42 for shoes. This was $14 less than twice what she spent for a blouse. How much was the blouse?
Solution. Every word problem has an unknown number. In this problem, it is the price of the blouse. Always let x represent the unknown number. That is, let x answer the question.
Let x, then, be how much she spent for the blouse. The problem states that "This" -- that is, $42 -- was $14 less than two times x.
Here is the equation:
2x − 14 = 42.
2x = 42 + 14 (Lesson 9)
= 56.
x = 56
2
= 28.
The blouse cost $28.
Example 2. There are b boys in the class. This is three more than four times the number of girls. How many girls are in the class?
Solution. Again, let x represent the unknown number that you are asked to find: Let x be the number of girls.
(Although b is not known -- it is an arbitrary constant -- it is not what you are asked to find.)
The problem states that "This" -- b -- is three more than four times x:
4x + 3 = b.
Therefore,
4x = b − 3
x = b − 3
4 .
The solution here is not a number, because it will depend on the value of b. This is a type of "literal" equation, which is very common in algebra.
Example 3. The whole is equal to the sum of the parts.
The sum of two numbers is 84, and one of them is 12 more than the other. What are the two numbers?
Solution. In this problem, we are asked to find two numbers. Therefore, we must let x be one of them. Let x, then, be the first number.
We are told that the other number is 12 more, x + 12.
The problem states that their sum is 84:
word problem = 84
The line over x + 12 is a grouping symbol called a vinculum. It saves us writing parentheses.
We have:
2x = 84 − 12
= 72.
x = 72
2
= 36.
This is the first number. Therefore the other number is
x + 12 = 36 + 12 = 48.
The sum of 36 + 48 is 84.
Example 4. The sum of two consecutive numbers is 37. What are they?
Solution. Two consecutive numbers are like 8 and 9, or 51 and 52.
Let x, then, be the first number. Then the number after it is x + 1.
The problem states that their sum is 37:
word problem = 37
2x = 37 − 1
= 36.
x = 36
2
= 18.
The two numbers are 18 and 19.
Example 5. One number is 10 more than another. The sum of twice the smaller plus three times the larger, is 55. What are the two numbers?
Solution. Let x be the smaller number.
Then the larger number is 10 more: x + 10.
The problem states:
2x + 3(x + 10) = 55.
That implies
2x + 3x + 30 = 55. Lesson 14.
5x = 55 − 30 = 25.
x = 5.
That's the smaller number. The larger number is 10 more: 15.
Example 6. Divide $80 among three people so that the second will have twice as much as the first, and the third will have $5 less than the second.
Solution. Again, we are asked to find more than one number. We must begin by letting x be how much the first person gets.
Then the second gets twice as much, 2x.
And the third gets $5 less than that, 2x − 5.
Their sum is $80:
word problem
5x = 80 + 5
x = 85
5
= 17.
This is how much the first person gets. Therefore the second gets
2x = 34.
And the third gets
2x − 5 = 29.
The sum of 17, 34, and 29 is in fact 80.
Example 7. Odd numbers. The sum of two consecutive odd numbers is 52. What are the two odd numbers?
Solution. First, an even number is a multiple of 2: 2, 4, 6, 8, and so on. It is conventional in algebra to represent an even number as 2n, where, by calling the variable 'n,' it is understood that n will take whole number values: n = 0, 1, 2, 3, 4, and so on.
An odd number is 1 more (or 1 less) than an even number. And so we represent an odd number as 2n + 1.
Let 2n + 1, then, be the first odd number. Then the next one will be 2 more -- it will be 2n + 3. The problem states that their sum is 52:
2n + 1 + 2n + 3 = 52.
We will now solve that equation for n, and then replace the solution in 2n + 1 to find the first odd number. We have:
4n + 4 = 52
4n = 48
n = 12.
Therefore the first odd number is 2 · 12 + 1 = 25. And so the next one is 27. Their sum is 52.
Problems
Problem 1. Julie has $50, which is eight dollars more than twice what John has. How much has John? (Compare Example 1.)
First, what will you let x represent?
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Do the problem yourself first!
The unknown number -- which is how much that John has.
What is the equation?
2x + 8 = 50.
Here is the solution:
x = $21