Question

complete the double number line diagram to show percentages of $50
money (dollars) 0 12.50 \boxed{} \boxed{} 50 62.50 \boxed{}
0 25% \boxed{} \boxed{} 100% 125% \boxed{}

Explanation:

Step1: Find the total amount

We know that 25% corresponds to $12.50. Let the total amount be LXI0. We use the proportion: LXI1. Solving for LXI2, we cross - multiply: LXI3, so LXI4. Wait, but later we see that 100% corresponds to $50? Wait, no, wait. Wait, 25% is $12.50, so 100% is \( 12.50\times4 = 50 \)? Wait, but in the money line, we have 0, 12.50, then some number, then some number, then 50, then 62.50, then \( n \). Wait, maybe the total is 50? Wait, no, let's re - examine.

Wait, the percentage line has 0, 25%, then a percentage, then a percentage, then 100%, then 125%, then a percentage. The money line has 0, 12.50, then \( a \), then \( b \), then 50, then 62.50, then \( n \).

We know that 25% of the total is $12.50. Let the total be LXI0. So LXI1, so LXI2. Wait, but 100% of LXI3 should be LXI4, so 100% corresponds to $50, which matches the money line (the fifth mark is 50 and the percentage mark is 100%). Then 125% of \( T \) is \( 1.25\times50 = 62.50 \), which also matches (money line: 62.50, percentage line: 125%).

Step2: Find the first missing money value (a)

The percentage between 25% and 100%: let's see the number of intervals. From 0 to 25% is one interval, then next interval: 25% to 50% (since 25% + 25% = 50%), then 50% to 75%? Wait, no, let's check the money line. The money line has marks at 0, 12.50, \( a \), \( b \), 50, 62.50, \( n \). The percentage line has 0, 25%, \( p1 \), \( p2 \), 100%, 125%, \( p3 \).

Since 25% is $12.50, 50% (which is 25%×2) should be \( 12.50\times2 = 25 \). So \( a = 25 \), and \( p1 = 50\% \).

Step3: Find the second missing money value (b)

75% (25%×3) of the total \( T = 50 \) is \( 0.75\times50=37.50 \). So \( b = 37.50 \), and \( p2 = 75\% \).

Step4: Find the last missing money value (n)

150% of \( T = 50 \) is \( 1.5\times50 = 75 \). Wait, the percentage after 125%: 125% + 25% = 150%? Wait, let's check the pattern. The percentage intervals: from 0 to 25% (25% increase), 25% to 50% (25% increase), 50% to 75% (25% increase), 75% to 100% (25% increase), 100% to 125% (25% increase), 125% to 150% (25% increase). So 150% of 50 is \( 0.15\times50 = 75 \)? Wait, no, 150% of 50 is \( 1.5\times50=75 \). And the percentage for \( n \) is 150%.

Step5: Fill in the percentage line

The first missing percentage (under the money value 25) is 50%, the second missing percentage (under the money value 37.50) is 75%, and the last missing percentage (under the money value \( n = 75 \)) is 150%.

Answer:

• Money line missing values: 25, 37.50, 75
• Percentage line missing values: 50%, 75%, 150%