Kyle has x 3-ounce blue marbles and a 5-ounce green marble. Lara has x 5-ounce green marbles and a 3-ounce blue marble. Is it possible for Kyle and Lara to have the same number of... Kyle has x 3-ounce blue marbles and a 5-ounce green marble. Lara has x 5-ounce green marbles and a 3-ounce blue marble. Is it possible for Kyle and Lara to have the same number of green marbles and the same total bag weight, y? Explain.
Understand the Problem
The question asks whether it's possible for Kyle and Lara to have the same number of green marbles and the same total bag weight, given the number and weight of their blue and green marbles. We need to determine if there's a value for 'x' that satisfies both conditions.
Answer
Yes, it is possible when $x=1$.
Answer for screen readers
Yes, it is possible. If $x = 1$, both Kyle and Lara have the same number of green marbles and the same total bag weight.
Steps to Solve
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Set up the equation for the number of green marbles Kyle has 1 green marble, and Lara has $x$ green marbles. For them to have the same number of green marbles, we must have $x = 1$
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Set up the equation for the total weight of Kyle's marbles Kyle has $x$ blue marbles weighing 3 ounces each and 1 green marble weighing 5 ounces. So, Kyle's total weight is $3x + 5$.
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Set up the equation for the total weight of Lara's marbles Lara has $x$ green marbles weighing 5 ounces each and 1 blue marble weighing 3 ounces. So, Lara's total weight is $5x + 3$.
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Set up the equation for the total weight to be the same For the total weights to be the same, we need $3x + 5 = 5x + 3$.
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Solve for $x$ from the weights equation Subtract $3x$ from both sides: $5 = 2x + 3$. Subtract 3 from both sides: $2 = 2x$. Divide both sides by 2: $x = 1$.
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Check if the x values are equal From step 1, we derived that $x=1$. From step 5, we also derived that $x=1$. Since both equations result in the same value of x, it is possible for Kyle and Lara to have the same number of green marbles and the same total bag weight.
Yes, it is possible. If $x = 1$, both Kyle and Lara have the same number of green marbles and the same total bag weight.
More Information
When $x=1$, Kyle has one 3-ounce blue marble and one 5-ounce green marble, for a total weight of 8 ounces. Lara has one 5-ounce green marble and one 3-ounce blue marble, for a total weight of 8 ounces.
Tips
A common mistake would be to not set up the equations correctly, especially for the total weights, mixing up the number of marbles and their weights. Another mistake would be to solve for $x$ independently for both conditions and not checking if the values of $x$ are the same.
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