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The difference between two numbers is 30. The sum of two-third of the first number and one-eleventh of the second number is 5. Find the product of the two numbers.​

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5 votes

Final answer:

To find the product of the two numbers, we need to solve the system of equations formed by the given information. The two numbers are 3 and -27, and their product is -81.

Step-by-step explanation:

To find the product of the two numbers, we need to solve the system of equations formed by the given information. Let's assume the first number is x and the second number is y.

From the first sentence, we have x - y = 30.

From the second sentence, we have (2/3)x + (1/11)y = 5.

To solve this system of equations, we can use the method of substitution or elimination. Let's use elimination:

Multiplying the second equation by 11 gives us (22/33)x + (1/11)y = 55/11.

Multiplying the first equation by 33 gives us 33x - 33y = 990.

Adding these two equations eliminates the y variable:

55/33x = 55/11 + 990.

Simplifying gives us 55/33x = 605/11.

Multiplying both sides by (33/55) gives us x = 605/11 * 33/55.

Simplifying further gives us x = 33/11 = 3.

Substituting this value back into the first equation gives us 3 - y = 30.

Simplifying gives us y = -27.

Therefore, the two numbers are 3 and -27, and their product is -81.

User Tessy Thomas
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8.3k points
7 votes

Answer:

26 and 32 are the two numbers, the product is 832

Step-by-step explanation:

User Erthalion
by
8.2k points

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