Twenty less than eight times a number is seventy six
1 answer:
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Answer:
200 resource books
800 fiction books
400 nonfiction books
Step-by-step explanation:
Let's define x as the amount of resource books that are in the library. As he has four times as many fiction books as resource books, that means he has 4*x fiction books.
We also know he has half as many nonfiction books as fiction books, that is 1/2*4*x = 2*x nonfiction books.
We just need to find out the value of x.
We know there are 1,400 books in total and there are just 3 types of books. Therefore, if we sum all of them, we get the 1,400.
Written in math language, that is
x + 4x + 2x = 1,400
7x = 1,400
We divide by 7 on both sides and we get
7/7x = 1,400/7
x = 200
Now we replace the x with 200 to know how many books he has of each type:
Resource books = x = 200
Fiction books = 4*x = 4*200 = 800
Nonfiction books = 2*x = 2*200 = 400
Therefore, there are 200 resource books, 800 fiction books and 400 nonfiction books in the library.
The tape diagram is attached as an image.
1.
<span>1.5x-1 > 6.5
1.5x>1+6.5
</span>1.5x>7.5, divide by 1.5
x>5, is represented by the region to the right of the vertical line x=5
2.
<span>7x+3 < -25
7x<-25-3
7x<-28, divide by 4:
x<-4
</span>x<-4, is represented by the region to the left of the vertical line x=-4
Answer: check the picture
<span>1.5x-1 > 6.5
1.5x>1+6.5
</span>1.5x>7.5, divide by 1.5
x>5, is represented by the region to the right of the vertical line x=5
2.
<span>7x+3 < -25
7x<-25-3
7x<-28, divide by 4:
x<-4
</span>x<-4, is represented by the region to the left of the vertical line x=-4
Answer: check the picture