Find two numbers whose product is 30 such that one of the numbers is 4 more than two times the other number.
A) {10, 6}, {-6, -10}
B) {10, 3}, {-10, -3}
C) {10, 3}, {-6, -5}
D) {10, -5}, {-6, 3}
E) none of these

Question

Quizplus · Accepted Answer

Let x be the smaller number, then the larger number is 2x+4. Thus, x(2x+4)=30, which simplifies to 2x^2+4x-30=0. Factoring gives (2x-6)(x+5)=0, so the possible values for x are 3 and -5/2. Plugging these values into the equation for the larger number yields the pairs {3,10} and {-5, -6}. Therefore, the correct choice is C, which contains the pair {10,3} and its negative counterpart {-6,-5}.

Find Two Numbers Whose Product Is 30 Such That One