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3 years ago

If the third of 6 consecutive numbers is 12, what is their sum?

Mathematics

1 answer:

andreev551 [17]3 years ago

6 0

The correct answer is 64

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Scott is reading two books at the same time to prepare for a report he is writing. So far, he has read 407 of the total number o

Hitman42 [59]

Answer:

The system of equations are

x+y=557

$\frac35x+\frac56 y=407$

The total pages in shorter book is 245

The total pages in longer book is 312

Step-by-step explanation:

Given that,

Scott has read 407 of the total number of 557 pages, which $\frac35$ of the shorter book and $\frac56$ of longer book.

Total number of pages of shorter book be x and longer book be y.

Then,

$\frac35$ page of the shorter book $=\frac35 x$

$\frac56$ pages of the longer book = $\frac56y$

So, he has read $=\frac35x+\frac 56y$

Total number of pages of both book is = x+y

According to the problem,

x+y=557.........(1)

$\frac35x+\frac56 y=407$ .......(2)

We can write equation (2) as

$\frac35x+\frac56 y=407$

$\Rightarrow \frac{18x+25y}{30}=407$

$\Rightarrow {18x+25y}=407\times 30$

$\Rightarrow {18x+25y}=12,210$ ......(3)

Now 18 times of equation (1) subtract from equation (3)

18x+25y=12210

18x+18y=10026

- - -

_______________

25y-18y=12,210-10,026

⇒7y=2,184

$\Rightarrow y=\frac{2184}{7}$

⇒y= 312

Plug y=312 in equation (1)

x+312=557

⇒x=557-312

⇒x=245

The total pages in shorter book is 245

The total pages in longer book is 312

5 0

3 years ago