Question

Given the equation y₁ y₂ y₃ y₄ = 30, each yi is an integer that is at least 2. What is the possible combination of y values that satisfies the equation?

a) 2, 3, 5, 1
b) 4, 2, 3, 1
c) 6, 1, 5, 1
d) 3, 2, 2, 5

Answer 1

The possible combination of y values that satisfies the equation y₁ y₂ y₃ y₄ = 30 is given by (option (d) 3, 2, 2, 5.

Step-by-step explanation:

To determine the combination of y values that satisfies the equation y₁ y₂ y₃ y₄ = 30, we need to factorize the number 30 into its prime factors and distribute them among the y values. The prime factorization of 30 is 2×3×5. To satisfy the condition that each yi is an integer at least 2, we can distribute these prime factors among the y values in a way that respects the constraints. Option (d) 3, 2, 2, 5 achieves this, as each value is at least 2, and their product equals 30 (option (d).

For example, with option (d), we have 3×2×2×5=60, which satisfies the equation. This combination respects the given conditions of integer values at least 2 and produces the desired product.

In conclusion, option (d) 3, 2, 2, 5 is the correct combination of y values that satisfies the equation y₁ y₂ y₃ y₄ = 30. This solution is derived by considering the prime factorization of 30 and distributing the factors among the y values while ensuring each yi is an integer at least 2.