1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Setler79 [48]
3 years ago
10

A, b, c and d are positive integers, such that a+b+ ab = 76, c+d+ cd = 54. Find (a+b+c+d)·a·b·c·d.

Mathematics
1 answer:
lutik1710 [3]3 years ago
6 0

Notice that

(1 + <em>x</em>)(1 + <em>y</em>) = 1 + <em>x</em> + <em>y</em> + <em>x y</em>

So we can add 1 to both sides of both equations, and we use the property above to get

<em>a</em> + <em>b</em> + <em>a b</em> = 76  ==>  (1 + <em>a</em>)(1 + <em>b</em>) = 77

and

<em>c</em> + <em>d</em> + <em>c d</em> = 54  ==>  (1 + <em>c</em>)(1 + <em>d</em>) = 55

Now, 77 = 7*11 and 55 = 5*11, so we get

<em>a</em> + 1 = 7  ==>  <em>a</em> = 6

<em>b</em> + 1 = 11  ==>  <em>b</em> = 10

(or the other way around, since the given relations are symmetric)

and

<em>c</em> + 1 = 5  ==>  <em>c</em> = 4

<em>d</em> + 1 = 11  ==>  <em>d</em> = 10

Now substitute these values into the desired quantity:

(<em>a</em> + <em>b</em> + <em>c</em> + <em>d</em>) <em>a</em> <em>b</em> <em>c</em> <em>d</em> = 72,000

You might be interested in
LOG 100 IS EQUAL TO WHAT
Marta_Voda [28]
Log 100 equals 2. If you use a scientific calculator it equals 2.
6 0
2 years ago
Read 2 more answers
The product of 4 and a number plus the product of 3 and the same number is 35. What is the number?
shutvik [7]
The number is 15,
I really don’t know if there’s such a strategy to find this out, I just used trial & error:
(a*4)+(a*3)=35
(5*4)+(5*3)=35
20+15=35
6 0
3 years ago
Question 25a answer plz x
nekit [7.7K]
Although it is warm it is not necessarily really hot that loads of children would not need to be in a paddling pool

hope I helped sorry if it wasn't the answer you was looking for
7 0
3 years ago
Read 2 more answers
Rudy collects baseball cards, and he currently has 300 cards. Starting tomorrow, he will purchase 1 pack of 15 baseball cards ev
Delvig [45]

Answer:

To find the number of cards, you must use the equation c = 300 + 17d. Collecting your known information in an organized form will be realllly helpful now and in the future. C represents the number of cards, while D represents the number of days!

Step-by-step explanation:

Starting with the original amount, which is 300---->

Here is the answer:

15 - 1 + 3 = 17 extra cards per day

3 0
3 years ago
The table shows the approximate diameters of four bacteria cells.
Wittaler [7]

Answer:B

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Other questions:
  • The news stations said that their polls showed that 9% of voters would vote in favor of passing the law 600 of the 6,342 voters
    6·1 answer
  • How many factors in the expression 8(x+4)(y+4)z^2+4z+7) have exactly two terms
    10·1 answer
  • Please help me with question 24 ‍♀️
    5·1 answer
  • HELP PLEASE DESPERATE!!
    14·2 answers
  • How is the interquartile range calculated?
    13·1 answer
  • A hiker averages 3/8 kilometers per hour. If he hikes for 1/3 hours, how many kilometers does he hike?
    14·1 answer
  • ABCDE is a pentagon. AM is the line of symmetry. How can you find all the inner angles?​
    14·1 answer
  • For the pair of similar triangles, find the value of x. <br><br> The value of x is .
    13·1 answer
  • What are three solutions of the inequality 29x+4&lt;76?
    5·2 answers
  • Eric was rock climbing. At one point, he stopped and climbed straight down 2\dfrac{1}{2}2
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!