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One number is [tex]\frac{3}{8}[/tex] of another number. The difference between the two numbers is 4.2. What is the lesser number?

A. 2.52
B. 6.72
C. 11.2
D. 1.52



Answer :

GinnyAnswer
Let's solve the problem step by step:

1. Define the variables:
Let [tex]\( x \)[/tex] be the greater number.
Let [tex]\( y \)[/tex] be the lesser number.

2. Formulate the relationship between the two numbers:
According to the problem, one number ([tex]\( y \)[/tex]) is [tex]\(\frac{3}{8}\)[/tex] of the other number ([tex]\( x \)[/tex]). Therefore, we can write:
[tex]\[ y = \frac{3}{8}x \][/tex]

3. Express the difference between the two numbers:
The problem also states that the difference between the greater number [tex]\( x \)[/tex] and the lesser number [tex]\( y \)[/tex] is 4.2. Thus, we write:
[tex]\[ x - y = 4.2 \][/tex]

4. Substitute the value of [tex]\( y \)[/tex] from the first equation into the second equation:
[tex]\[ x - \frac{3}{8}x = 4.2 \][/tex]

5. Simplify the equation:
[tex]\[ \frac{5}{8}x = 4.2 \][/tex]

6. Solve for [tex]\( x \)[/tex]:
[tex]\[ x = \frac{4.2}{\frac{5}{8}} = \frac{4.2 \times 8}{5} = 6.72 \][/tex]
Therefore, the greater number [tex]\( x \)[/tex] is 6.72.

7. Determine the lesser number [tex]\( y \)[/tex]:
Using the relationship [tex]\( y = \frac{3}{8}x \)[/tex]:
[tex]\[ y = \frac{3}{8} \times 6.72 = 2.52 \][/tex]

So, the lesser number is [tex]\( 2.52 \)[/tex].

Out of the given options, the correct answer is:

[tex]\[ \boxed{2.52} \][/tex]
sqdancefan

Answer:

  A. 2.52

Step-by-step explanation:

You want the smaller of two numbers whose difference is 4.2 with the requirement the smaller is 3/8 of the larger.

Ratios

If the smaller is 3/8 of the larger, their ratio is ...

  3 : 8

Then the ratio of the smaller to the difference is ...

  3 : (8 -3) = 3 : 5

That is, the smaller number is 3/5 of the difference:

  (3/5) × 4.2 = 2.52

The lesser number is 2.52, choice A.

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