Question

some beaches are protected sanctuaries so that green sea turtles can come to lay eggs without being disturbed. this year, there are 234 nesting turtles at a sanctuary. this is 10% less than the number of nesting turtles at the same sanctuary last year 8. create at least two representations that show how many nesting turtles were at the sanctuary last year. double number line equation

Explanation:

Step1: Define the variable

Let \( x \) be the number of nesting turtles last year.

Step2: Set up the equation

This year's number (234) is 10% less than last year's, so \( x - 0.1x = 234 \) or \( 0.9x = 234 \).

Step3: Solve for \( x \)

Divide both sides by 0.9: \( x=\frac{234}{0.9}=260 \).

Double Number Line:

• Draw a number line for last year (let it range from 0 to 300 for example) and this year.
• Mark that 100% of last year is \( x \), so 90% (since 10% less) is 234.
• Divide the last year line into 10 equal parts (each 10%). Since 9 parts (90%) correspond to 234, 1 part is \( \frac{234}{9} = 26 \), so 10 parts (100%) is \( 26\times10 = 260 \).

Answer:

Last year, there were 260 nesting turtles. The two representations are the equation \( 0.9x = 234 \) (solved to \( x = 260 \)) and the double number line showing 90% of last year's turtles is 234, leading to 100% (last year) being 260.