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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 = 72However, as the numbers are consecutive even integers we also know that:b = a - 2c = a - 4d = a - 6thus 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 = 728a = 96a = 12Once we have a value for "a" we have a value for all the variables:a = 12b = 10c = 8d = 6As a proof, if we wish, we can substitute these values back into the original equation to get:ab - cd = 72(12 * 10) - (8 * 6) = 72120 - 48 = 72.
The square of certain number exceeds 24 by 5 times the numberwhat is the number?
120 there the number
