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1.The product of 3 more than a number and 5 more than the number is 35. find
the number.
2.The product of a number diminished by 2 and 10 less than the number is -15.find the number.
3. The product of two consecutive integers is 110.find the integers.
4.Two consecutive positive even numbers have a product that is 120.what are the numbers?
5. One positive number is 3 more than another.their product is 180.find the numbers.
1.The product of 3 more than a number and 5 more than the number is 35. find
the number.
2.The product of a number diminished by 2 and 10 less than the number is -15.find the number.
3. The product of two consecutive integers is 110.find the integers.
4.Two consecutive positive even numbers have a product that is 120.what are the numbers?
5. One positive number is 3 more than another.their product is 180.find the numbers.
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Step-by-step explanation:
1. (3 + n)(5 + n) = 35
VIA FOIL METHOD
15 + 3n + 5n +n² = 35
n² + 8n + 15 = 35
n² + 8n + 15 - 15 = 35 - 15
n² + 8n = 20
VIA COMPLETING THE SQUARE
n² + 8n + (8/2•1)² = 20 + (8/2•1)²
n² + 8n + (4)² = 20 + (4)²
n² + 8n + 16 = 20 + 16
(n + 4)² = 36
√(n + 4)² = √36
n + 4 = 6
n + 4 - 4 = 6 -4
n = 2 ANSWER
CHECK:
(3 + n)(5 + n) = ?
(3 + 2)(5 + 2) = ?
(5)(7) = 35 ✓
2. (n - 2)(10 - n) = -15
VIA FOIL METHOD
10n - n² - 20 + 2n = -15
-n² + 10n + 2n - 20 = -15
-n² + 12n - 20 = -15
-1(n² - 12n + 20)/ -1 = -15/-1
n² - 12n + 20 = 15
n² - 12n + 20 - 20 = 15 - 20
n² - 12n = - 5
VIA COMPLETING THE SQUARE
n² - 12n +(-12/2•1)² = -5 +(-12/2•1)²
n² - 12n + (-6)² = -5 + (-6)²
n² - 12n + 36 = -5 + 36
(n - 6)² = 31
√(n - 6)² = √31
n - 6 = √31
n - 6 + 6 = √31 + 6
n = 6 + √31 ANSWER
CHECK:
(n - 2)(10 - n) = ?
[(6 + √31) - 2][10 - (6 + √31)] = -15 ✓