0
What are 4 consecutive even integers where the product of the two smaller number is 72 less than the product of the two larger numbers?
12, 10, 8 and 6 (in descending order).
Let the highest number equal a.
We are told that ab - cd = 72
However, as the numbers are consecutive even integers we also know that:
b = a - 2
c = a - 4
d = a - 6
thus we can use this to write the above equation in terms of only one variable, a, as:
(a * (a - 2)) - ((a-4) * (a-6)) = 72
(a2 - 2a) - (a2 - 10a + 24) = 72 (Remember that as we expand the second bracket in the next step we will multiply each term by the minus outside the bracket giving:)
a2 - 2a - a2 + 10a - 24 = 72 (Now we can continue to simplify to get:)
8a - 24 = 72
8a = 96
a = 12
Once we have a value for "a" we have a value for all the variables:
a = 12
b = 10
c = 8
d = 6
As a proof, if we wish, we can substitute these values back into the original equation to get:
ab - cd = 72
(12 * 10) - (8 * 6) = 72
120 - 48 = 72.
What else can I help you with?
Find 4 consecutive even integers where the product of the smaller two numbers is 56 less than the product of the two larger numbers?
4,6,8,10
Find four consecutive odd integers if the product of the two smaller integers is 112 less than the product of the two large integers?
The numbers are 11, 13, 15 and 17.
The product of 2 positive consecutive even integers is 48 What is the smaller number?
The product of 2 consecutive positive number is 48. Find the 2 numbers
The sum of two consecutive integers is 63. The smaller of the two numbers is?
The smaller of the two numbers is 31.
Find 3 consecutive odd numbers where the product of the two smaller numbers is 22 less than the product of the two larger numbers?
In 'normal' arithmetic, there is no solution of 3 consecutive odd numbers where the product of the smaller two is 22 less than that of the larger two. For instance difference in products for 1-3-5 is 12, for 3-5-7 it is 20, and for 5-7-9 it is 28. The series steps by 8 integers for each set of 3 odd numbers investigated.
Find 4 consecutive even integers where the product of the smaller two numbers is 56 less than the product of the two larger numbers?
4,6,8,10
Find four consecutive odd integers if the product of the two smaller integers is 112 less than the product of the two large integers?
The numbers are 11, 13, 15 and 17.
The product of 2 positive consecutive even integers is 48 What is the smaller number?
The product of 2 consecutive positive number is 48. Find the 2 numbers
Find 4 consecutive even integers where the product of the two smaller numbers is 72 less than the product of the larger two integers?
They are 6, 8, 10 and 12.
The sum of two consecutive integers is 63. The smaller of the two numbers is?
The smaller of the two numbers is 31.
Two consecutive positive integers have a product of 156 find the smaller integer?
13 and 12 are the two integers that have the product of 156 and 12 is the smaller of the two.
The product of 2 consecutive even integers is 48 what is the smaller number?
Smaller number is '6'
The product of 2 positive consecutive integers is 48. what is the smaller number?
It is 23.
What are the products of two consecutive positive integers?
The product of two consecutive positive integers can be found by multiplying the smaller integer by the larger integer. If the smaller integer is represented as ( n ), then the larger integer would be ( n + 1 ). Therefore, the product of two consecutive positive integers is ( n \times (n + 1) ).
Find two consecutive integers whose sum is eighty nine let x be the smaller of these two integers what is the larger of these two consecutive integers what r the two numbers?
44 & 45
What is the largest of 3 consecutive negative integers if the product of the larger two integers is 5 more than the smaller integer?
-1
What are 4 consecutive even integers where the product of the smaller two numbers is 72 less than the product of the two larger numbers?
6 x 8 = 48 10 x 12 = 120 120 - 48 = 72
