SOLUTION: The sum of two numbers is 23. If the product of the two numbers must be greater than 76, what pairs of numbers satisfy the conditions if both numbers are integers?

Question 901220: The sum of two numbers is 23. If the product of the two numbers must be greater than 76, what pairs of numbers satisfy the conditions if both numbers are integers?

Found 2 solutions by JulietG, josgarithmetic:
Answer by JulietG(1812) (Show Source): You can put this solution on YOUR website!
A + B = 23
A * B > 76
Let's look at possible pairs that satisfy the first equation, and then whether they satisfy the second.
{23,0} = 23*0=0
{22,1} = 22*1=22
{21,2} = 21*2=42
{20,3} = 20*3=60
{19,4} = 19*4=76 [don't let this trick you because it's GREATER THAN 76]
{18,5} = 18*5 =90
{17,6} = 17*6 = 102
{16,7} = 16*7 = 112
{15,8} = 15*8 = 120
{14,9} = 14*9 = 126
{13,10} = 13*10 = 130
{12,11} = 12*11 = 132

The pairs with numbers reversed also satisfy the equation. {11,12} rather than {12,11}

Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
x and y. They are INTEGERS.
, and .

; substitute into the inequality.

You want integers between 4 and 19. You do not want these two values included,
because the problem specified a strict inequality, product GREATER than 76.
5 & 18 ? Yes.
6 & 17 ? Yes.
.
.
11&12? Yes.

ANSWER: Lowest number 5; highest number 18,
whose sum is 23.

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