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# Systems of equations with elimination: Sum/difference of numbers

Sal finds two numbers that sum to 70 and have a difference of 24. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• someone please explain this to me
• Like Sir Cumference said, just watch the previous videos. You shouldn't skip around otherwise you'll miss something...
• at if we assume that y is larger than x then, by calculation, solution is (23, 47). Is this valid?
• actually yes
(1 vote)
• Can you use the elimination method to find out the two "sum & product" numbers? And if so, how?

Example of a worded question: The sum of two numbers is -42 and the product is -1. What are the two numbers?

Another example: The product of two numbers is equivalent to hundred-eight. The sum of the same two numbers is equal to twenty-four. Find out the two numbers.
• 6 * (-7) = -42
6 + (-7) = -1
The two numbers are: 6 and -7

Well I guess the addition elimination method can't be used in this case.
(1 vote)
• in the question shouldn't it say find the one number not two numbers?
• Doesn't have to be. This is more like a complex way of elimination. But what you're thinking of is correct too.
• What is the missing number 1,16,-----100,169
• That would 49. Each number is the square of 1, 4, 7, 10 ,13 respectively.
• i watched tis video and it confused me all the way to the end can some onr use english to help me?
• I doubt that anyone can type an answer here that will seem clearer to you than the video. I would suggest you watch the video again, slowly, and make sure you understand what is happening at each step. Maybe do that a couple of times. Keep at it and you will get it. If you are still struggling, a teacher should be able to help you.
• can someone please explain this type of eqation to me, its from one of the exersise things i just dont get it?
EX: Ishaan sells magazine subscriptions and earns \$10 for every new subscriber he signs up. Ishaan also earns a \$31 weekly bonus regardless of how many magazine subscriptions he sells.

If Ishaan wants to earn at least \$74 this week, what is the minimum number of subscriptions he needs to sell?
• Ishaan get \$10 for every new subscriber, so let x represent the number of new subscribers. So if there were 5 new subscribers, 10(5) = 50 dollars he would earn given \$10 for each new subscriber. However, he also earns a weekly bonus of \$31, regardless of how many he sells (just for going out on the job and trying :)) So, we could represent his weekly earnings potential by saying 10x + 31. Therefore, if he sold 1 subscription, 10(1) + 31 = \$41; if he sold 2 subscriptions,
10(2) + 31 = \$51, and so on. Since I know Ishaan wants to earn at least \$74, I would write 10x + 31 = 74 and solve. Subtraction 31 from both sides gives me 10x=43; dividing both sides by 10 gives me 4.3 So, if he only sold 4 subscriptions, he would earn \$71 [ 10(4) +31 = \$71] and if he sold 5 subscriptions he would earn \$81 [10(5) + 31 = \$81]. Therefore, since he wants to earn at least \$74, and he cannot sell a part of a subscription, he must sell 5 new subscriptions in order to earn \$74.
• One number is 5 more than 4 times the other and their sum is 10. Find the numbers
• Let us take the first number as x
according to question, we find the second number as=4x+5
Now adding both and equating to their sum we have,
4x+5+x=10
5x=5
x=1

so the two numbers are 1, 9.
Hope i was successful in solving your problem effectively...