At Westonci.ca, we connect you with the best answers from a community of experienced and knowledgeable individuals. Experience the ease of finding precise answers to your questions from a knowledgeable community of experts. Get detailed and accurate answers to your questions from a dedicated community of experts on our Q&A platform.
Sagot :
To determine the number of children and adults at the museum, we need to solve the given system of equations:
[tex]\[ \begin{aligned} 12x + 25y &= 9014 \\ x + y &= 450 \end{aligned} \][/tex]
Here's the step-by-step solution to this problem:
1. Express one variable in terms of the other using the simpler equation (second equation).
From the equation [tex]\( x + y = 450 \)[/tex], we can solve for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]:
[tex]\[ y = 450 - x \][/tex]
2. Substitute this expression into the first equation.
Substitute [tex]\( y = 450 - x \)[/tex] into the equation [tex]\( 12x + 25y = 9014 \)[/tex]:
[tex]\[ 12x + 25(450 - x) = 9014 \][/tex]
3. Simplify and solve for [tex]\( x \)[/tex].
Distribute and combine like terms:
[tex]\[ 12x + 11250 - 25x = 9014 \][/tex]
Simplify the equation:
[tex]\[ -13x + 11250 = 9014 \][/tex]
Isolate [tex]\( x \)[/tex] by subtracting 11250 from both sides:
[tex]\[ -13x = 9014 - 11250 \][/tex]
[tex]\[ -13x = -2236 \][/tex]
Divide both sides by -13 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{2236}{13} \approx 172 \][/tex]
4. Find [tex]\( y \)[/tex] using the value of [tex]\( x \)[/tex].
Substitute [tex]\( x = 172 \)[/tex] back into the equation [tex]\( y = 450 - x \)[/tex]:
[tex]\[ y = 450 - 172 = 278 \][/tex]
Therefore, the number of children ([tex]\(x\)[/tex]) that visited the museum is approximately [tex]\(172\)[/tex], and the number of adults ([tex]\(y\)[/tex]) is approximately [tex]\(278\)[/tex].
5. Verify the result using the choices provided.
The choices given are: [tex]\(275\)[/tex], [tex]\(450\)[/tex], [tex]\(350\)[/tex], [tex]\(200\)[/tex], [tex]\(300\)[/tex], [tex]\(175\)[/tex]. We can confirm that none of these choices exactly fit [tex]\(172\)[/tex] for children or [tex]\(278\)[/tex] for adults, meaning the solution ([tex]\(172\)[/tex] children and [tex]\(278\)[/tex] adults) is neither overestimated nor underestimated based on the given constraints.
In conclusion, approximately [tex]\(172\)[/tex] children and [tex]\(278\)[/tex] adults visited the museum.
[tex]\[ \begin{aligned} 12x + 25y &= 9014 \\ x + y &= 450 \end{aligned} \][/tex]
Here's the step-by-step solution to this problem:
1. Express one variable in terms of the other using the simpler equation (second equation).
From the equation [tex]\( x + y = 450 \)[/tex], we can solve for [tex]\( y \)[/tex] in terms of [tex]\( x \)[/tex]:
[tex]\[ y = 450 - x \][/tex]
2. Substitute this expression into the first equation.
Substitute [tex]\( y = 450 - x \)[/tex] into the equation [tex]\( 12x + 25y = 9014 \)[/tex]:
[tex]\[ 12x + 25(450 - x) = 9014 \][/tex]
3. Simplify and solve for [tex]\( x \)[/tex].
Distribute and combine like terms:
[tex]\[ 12x + 11250 - 25x = 9014 \][/tex]
Simplify the equation:
[tex]\[ -13x + 11250 = 9014 \][/tex]
Isolate [tex]\( x \)[/tex] by subtracting 11250 from both sides:
[tex]\[ -13x = 9014 - 11250 \][/tex]
[tex]\[ -13x = -2236 \][/tex]
Divide both sides by -13 to solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{2236}{13} \approx 172 \][/tex]
4. Find [tex]\( y \)[/tex] using the value of [tex]\( x \)[/tex].
Substitute [tex]\( x = 172 \)[/tex] back into the equation [tex]\( y = 450 - x \)[/tex]:
[tex]\[ y = 450 - 172 = 278 \][/tex]
Therefore, the number of children ([tex]\(x\)[/tex]) that visited the museum is approximately [tex]\(172\)[/tex], and the number of adults ([tex]\(y\)[/tex]) is approximately [tex]\(278\)[/tex].
5. Verify the result using the choices provided.
The choices given are: [tex]\(275\)[/tex], [tex]\(450\)[/tex], [tex]\(350\)[/tex], [tex]\(200\)[/tex], [tex]\(300\)[/tex], [tex]\(175\)[/tex]. We can confirm that none of these choices exactly fit [tex]\(172\)[/tex] for children or [tex]\(278\)[/tex] for adults, meaning the solution ([tex]\(172\)[/tex] children and [tex]\(278\)[/tex] adults) is neither overestimated nor underestimated based on the given constraints.
In conclusion, approximately [tex]\(172\)[/tex] children and [tex]\(278\)[/tex] adults visited the museum.
We hope our answers were useful. Return anytime for more information and answers to any other questions you have. We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.