Answer: It's the second option
Step-by-step explanation:
Answer: Choice B)
2x+5(2x+3) = 3
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Reasoning:
We start with the second equation 2x+5y = 3
Since y = 2x+3 from the first equation, we can replace every copy of y with (2x+3). This replacement is valid because y and 2x+3 are the same.
So that's how we go from 2x+5y = 3 to 2x+5(2x+3) = 3
This replacement is done to get rid of the y variable, and it allows us to solve for x later on.
Answer: The loser's card shows 6.
Explanation: Let's start by naming the first student A and the second student B.
Since the product of A and B are either 12, 15, or 18, let's list every single possibility, the first number being A's number and the second number being B's number.
1 12
1 15
1 18
2 6
2 9
3 4
3 5
3 6
4 3
5 3
6 2
6 3
9 2
12 1
15 1
18 1
Now, the information says that A doesn't know what B has, so we can immediately cross off all of the combinations that have the integer appearing once and once ONLY off, because if it happened once only, A would know of it straight away. Now, our sample space becomes much smaller.
1 12
1 15
1 18
2 6
2 9
3 4
3 5
3 6
6 2
6 3
Using this same logic, we know that we can cross off all of the digits that occur only once in B's column.
2 6
3 6
Now, A definitely knows what number B has because there is only one number left in B. Hence, we can conclude that the loser, B, has the integer 6.
See picture for answer and solution steps.
Answer:
Step-by-step explanation:
