The giraffes at the Liberia zoo eat 75 pounds of food per day, and 52.5 pounds per day comes from acacia leaves. How much of their diet comes from other types of leaves?

Julia, the zookeeper, used the equation [tex]52.5 + x = 75[/tex] to find the answer. Which equation is an equivalent equation that can be used to solve the problem?

A. [tex]52.5 + 75 = x[/tex]

B. [tex]x + 75 = 52.5[/tex]

C. [tex]75 - 52.5 = x[/tex]

D. [tex]x - 52.5 = 75[/tex]



Answer :

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.