The difference of two numbers is 4 and their product is 60. Find the numbers.
2 answers:
Answer:
x = 10; y = 6
Step-by-step explanation:
Let's list the factors of 60 because the product of those numbers is 60.
- ⇒ Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
<u>The following possibilities of x and y are possible using (x × y = 60):</u>
- 60 and 1 ⇒ x = 60; y = 1 ⇒ 60 × 1 = 60
- 30 and 2 ⇒ x = 30; y = 2 ⇒ 30 × 2 = 60
- 20 and 3 ⇒ x = 20; y = 3 ⇒ 20 × 3 = 60
- 15 and 4 ⇒ x = 15; y = 4 ⇒ 15 × 4 = 60
- 12 and 5 ⇒ x = 12; y = 5 ⇒ 12 × 5 = 60
- 10 and 6 ⇒ x = 10; y = 6 ⇒ 10 × 6 = 60
<u>Let's check each possibilities using the equation (x - y = 4):</u>
- 60 and 1 ⇒ 60 - 1 = 59 ≠ 4
- 30 and 2 ⇒ 30 - 2 = 28 ≠ 4
- 20 and 3 ⇒ 20 - 3 = 17 ≠ 4
- 15 and 4 ⇒ 15 - 4 = 11 ≠ 4
- 12 and 5 ⇒ 12 - 5 = 7 ≠ 4
- 10 and 6 ⇒ 10 - 6 = 4 = 4 (Correct)
Thus, the values of x and y are 10 and 6 <u>respectively.</u>
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30 and 60
the only plausible answer would be 6 and 10
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