EXERCISES Directions: Solve the following problems. Write your complete solutions in your activity notebook or answer sheet. 1. The product of two consecutive integers is 210. Find the integers. 2. The sum of a number and its square is 156. Find the numbers. 3. A room contains 112 chairs. The number of chairs per row is five less than three times the number of rows. Find the number of chairs per row. INPUT MENUIplase help me and give me the correct Answer ​

Answer:1)  The two possible pairs are -15, -14 and 14, 15.2.  x = 12 or x = -133.  16 chairs/rowStep-by-step explanation:1.  The product of two consecutive integers is 210.Let the smallest integer be x.  The next consecutive integer would be x + 1.The product is 210, so we can write:    (x)*(x+1) = 210x^2 + x = 210x^2 + x - 210 = 0Let's see if we can factor this instead of using the quadratic equation.  We know the factors must be whole numbers, since that's how we defined them.  We need two numbers that:   a)  Multiply to -210   b)  Add to +1 (the coefficient of x)Let's try pairs of factors of 210:−14 × 15 = −210−14×15 = −210 and −14+15 = 1These seem to work, so we can write:  x^2 + x - 210 = (x + 15) (x - 14)So x can be either -15 or + 14Let's try x = -15.  x + 1 would be - 14(-15)*(-14) = 210  That works.  Now let's try x = 14.  x + 1 = 15 (14)*(15) = 210  That also works. The two possible pairs are -15, -14 and 14, 15.====2. The sum of a number and its square is 156. Find the numbers. Let the "number" be x.    "sum of a number and its square is 156"       x + x^2 = 156       x*2 + x - 156 = 0    We need two numbers that:       -   Multiply to -156, and       -  Add to +1Try factor pairs of 156:−12 × 13 = − 156    checks    and −12+13=1    checks(x - 12)*(x + 13) = x^2 + x - 156The answers are x = 12 or x = -13.3. A room contains 112 chairs. The number of chairs per row is five less than three times the number of rows. Find the number of chairs per row.a)  Let the number of rows be x.b)  The number of chairs per row is:  3x - 5c)  Total chairs = rows × chairs per row:         112 chairs = x*(3x - 5)Step 1: Expand and move all terms to one side:      3x^2  - 5x = 112      3x^2  − 5x - 112 = 0Solve with the quadratic equation:  a = 3, b = -5, c = -112   x = (-b±[tex]\sqrt{b^2-4ac}[/tex])/2a   x = (5±[tex]\sqrt{[(-5)^2-4*3*(-112)]}[/tex])/2*3  x = 7 and x = -(16/3)-(16/3) makes no sense, so drop that value and go with x = 7There are 7 rowsAt 112 chairs, that makes (112 chairs)/( 7 rows) or 16 chairs/row.

Answered by rspill6 | 2025-08-07