Alright, let's work through this step-by-step.
Given:
- The giraffes eat a total of 75 pounds of food per day.
- Out of the 75 pounds, 52.5 pounds come from acacia leaves.
- We need to determine how much of their diet comes from other types of leaves.
To find this, Julia used the equation:
[tex]\[ 52.5 + x = 75 \][/tex]
where:
- [tex]\( 52.5 \)[/tex] is the weight of acacia leaves eaten.
- [tex]\( x \)[/tex] is the weight of other types of leaves eaten.
- [tex]\( 75 \)[/tex] is the total weight of food eaten.
The goal is to isolate [tex]\( x \)[/tex], which represents the weight of other leaves.
To isolate [tex]\( x \)[/tex]:
1. Subtract 52.5 from both sides of the equation to get [tex]\( x \)[/tex] by itself on one side.
[tex]\[ 52.5 + x - 52.5 = 75 - 52.5 \][/tex]
Simplifying:
[tex]\[ x = 75 - 52.5 \][/tex]
Thus, the equivalent equation that can be used to solve the problem is:
[tex]\[ x = 75 - 52.5 \][/tex]
Among the given choices:
1. [tex]\( 52.5 + 75 = x \)[/tex] (Incorrect)
2. [tex]\( x + 75 = 52.5 \)[/tex] (Incorrect)
3. [tex]\( 75 - 52.5 = x \)[/tex] (Correct)
4. [tex]\( x - 52.5 = 75 \)[/tex] (Incorrect)
The correct equivalent equation is:
[tex]\[ 75 - 52.5 = x \][/tex]
So, the answer is:
[tex]\[ \boxed{75 - 52.5 = x} \][/tex]
Given the result:
[tex]\[ 75 - 52.5 = 22.5 \][/tex]
Thus, [tex]\( x = 22.5 \)[/tex]. This means that 22.5 pounds of the giraffes' diet comes from other types of leaves.
