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Yuri [45]
3 years ago
10

A bookcase has two shelves. The top shelf has 10 more than 1/3 the number of books on the bottom shelf. There are 12 books on th

e bottom shelf. How many books are on the top shelf?
a.4
b.14
c.40
d.46
Show your work below!!!
Mathematics
1 answer:
kobusy [5.1K]3 years ago
6 0

Answer: b.14

Step-by-step explanation:

We have two shelves, the top shelf s_{t} and the bottom shelf s_{b}.

Now, firstly we are told the top shelf has 10 more than 1/3 the number of books on the bottom shelf. This can be expressed as:

s_{t}=10+\frac{1}{3}s_{b} (1)

Then, we are told there are 12 books on the bottom shelf:

s_{b}=12 (2)

Substituting (2) in (1):

s_{t}=10+\frac{1}{3}(12) (3)

s_{t}=10+\frac{12}{3} (4)

s_{t}=14 (5) This is the number of books on the top shelf

Hence, the correct option is b.

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Step-by-step explanation:

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2 years ago
What's the answer to this? and please explain.
vichka [17]
<h3>Answer: No, there isn't enough ribbon</h3>

===========================================================

Use this formula

a & b/c = (a*c+b)/c

to convert from a mixed number to an improper fraction

So,

a & b/c = (a*c+b)/c

3 & 3/4 = (3*4+3)/4

3 & 3/4 = 15/4

---------------------------------------------------

Next, we add the fractions 15/4 and 5/6. The denominators aren't the same, so we can't add right away. We need to get the denominators to the LCD.

In this case, the LCD is 4*6 = 24

  • The fraction 15/4 becomes 90/24 after multiplying top and bottom by 6.
  • The fraction 5/6 becomes 20/24 after multiplying top and bottom by 4

Now we can add the fractions:

90/24+20/24 = (90+20)/24 = 110/24

---------------------------------------------------

So far, we've added the 3&3/4 portion to the 5/6 portion to get the result 110/24

The last thing to do is to add on the two 1/3 ft pieces, which means we're adding on 2/3 of a foot

2/3 = 16/24 after multiplying top and bottom by 8

Add this to the result of the last section

110/24+16/24 = (110+16)/24 = 126/24

---------------------------------------------------

From here, we convert the improper fraction 126/24 to decimal form

Using a calculator, you should find that 126/24 = 5.25

The result is larger than 5, which means she used too much ribbon. There won't be enough ribbon to do everything she wants to do.

---------------------------------------------------

The shortcut we can take is to type the following into the calculator

3+3/4+5/6+2/3

doing so should lead to 5.25

5 0
3 years ago
Read 2 more answers
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hope it helps.......

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