Let’s solve this step by step.
We are told:
- The point (p, r) lies on the line y = x + b.
- The point (2p, 5r) lies on the line y = 2x + b.
- p ≠ 0.
- We need to find the value of r/p.
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Step 1: Use the first point in the first equation.
Since (p, r) is on y = x + b, plug in x = p and y = r:
→ r = p + b ...(Equation 1)
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Step 2: Use the second point in the second equation.
Since (2p, 5r) is on y = 2x + b, plug in x = 2p and y = 5r:
→ 5r = 2*(2p) + b
→ 5r = 4p + b ...(Equation 2)
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Step 3: Subtract Equation 1 from Equation 2 to eliminate b.
Equation 2: 5r = 4p + b
Equation 1: r = p + b
Subtract Equation 1 from Equation 2:
(5r - r) = (4p + b) - (p + b)
→ 4r = 3p
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Step 4: Solve for r/p.
Divide both sides by p (since p ≠ 0):
→ 4r/p = 3
→ r/p = 3/4
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Final Answer:
B) 3/4
Parent Tip: Review the logic above to help your child master the concept of sat math prep worksheet.
