Answer :
To solve the problem, let's break down the information and each of the provided options:
First, the problem tells us that 45% of some number is 83. Mathematically, this means:
[tex]\[ 0.45 \times \text{some number} = 83 \][/tex]
To find the number, we solve for it by dividing 83 by 0.45:
[tex]\[ \text{some number} = \frac{83}{0.45} \][/tex]
Now let's examine each option to see which statement is not true:
a. This problem asks, "45% of what number equals 83?"
- This statement is true because it accurately restates the given problem.
b. This problem can be solved by evaluating the expression [tex]\( 83(0.45) \)[/tex].
- This statement is not true. Calculating [tex]\( 83(0.45) \)[/tex] would give us [tex]\( 37.35 \)[/tex], which doesn't help us find the original number. We need to divide, not multiply.
c. This problem can be solved by evaluating the expression [tex]\( 83 \div 0.45 \)[/tex].
- This statement is true. Dividing 83 by 0.45 is the correct mathematical operation to find the original number.
d. This problem can be solved by evaluating the expression [tex]\( 83 \div \frac{9}{7n} \)[/tex].
- This statement is not true. The expression [tex]\( 83 \div \frac{9}{7n} \)[/tex] is incorrect and unrelated to the original problem.
Based on this analysis, the statements that are not true are b and d.
First, the problem tells us that 45% of some number is 83. Mathematically, this means:
[tex]\[ 0.45 \times \text{some number} = 83 \][/tex]
To find the number, we solve for it by dividing 83 by 0.45:
[tex]\[ \text{some number} = \frac{83}{0.45} \][/tex]
Now let's examine each option to see which statement is not true:
a. This problem asks, "45% of what number equals 83?"
- This statement is true because it accurately restates the given problem.
b. This problem can be solved by evaluating the expression [tex]\( 83(0.45) \)[/tex].
- This statement is not true. Calculating [tex]\( 83(0.45) \)[/tex] would give us [tex]\( 37.35 \)[/tex], which doesn't help us find the original number. We need to divide, not multiply.
c. This problem can be solved by evaluating the expression [tex]\( 83 \div 0.45 \)[/tex].
- This statement is true. Dividing 83 by 0.45 is the correct mathematical operation to find the original number.
d. This problem can be solved by evaluating the expression [tex]\( 83 \div \frac{9}{7n} \)[/tex].
- This statement is not true. The expression [tex]\( 83 \div \frac{9}{7n} \)[/tex] is incorrect and unrelated to the original problem.
Based on this analysis, the statements that are not true are b and d.
