Question5. A weightlifter is adding plates of equal weight to a bar. The table below shows the total weight, including the bar, that he will lift depending on the total number of plates on the bar.
\begin{tabular}{|c|c|}
\hline Number of Plates & \begin{tabular}{c}
Total Weight in \\
Pounds
\end{tabular} \\
\hline 2 & 115 \\
\hline 4 & 185 \\
\hline 6 & 255 \\
\hline 8 & 325 \\
\hline
\end{tabular}
Based on this information, which statement is true?
A. The bar weighs 35 pounds without any plates.
B. The bar weighs 70 pounds without any plates.
C. The bar weighs 45 pounds without any plates.
D. The bar weighs 25 pounds without any plates.
Studdy Solution
STEP 1
1. The relationship between the number of plates and the total weight is linear.
2. Let be the weight of each plate.
3. Let be the weight of the bar without any plates.
4. We need to determine the values of and to find the weight of the bar.
STEP 2
1. Set up a system of linear equations based on the given data.
2. Solve the system of equations to find the weight of one plate and the weight of the bar.
STEP 3
Set up the first equation using the data point for 2 plates.
STEP 4
Set up the second equation using the data point for 4 plates.
STEP 5
Set up the third equation using the data point for 6 plates.
STEP 6
Set up the fourth equation using the data point for 8 plates.
STEP 7
Subtract the first equation from the second equation to eliminate and solve for .
STEP 8
Verify the value of by substituting it into the other equations to ensure consistency.
STEP 9
Verify by substituting and into the fourth equation to ensure consistency.
SOLUTION:
Based on the calculations, the weight of the bar without any plates is 45 pounds.
Therefore, the true statement is:
C. The bar weighs 45 pounds without any plates.
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