A number n is multiplied by 5/8. The product is subtracted by 2/3. The result 7/12, what is n.
Translate the English into Math, after all Mathematics is a language.
"A number n is multiplied by 5/8" --- (5/8)n
"The product is subtracted by 2/3", poorly worded, I will assume
you mean -----> (5/8)n - 2/3
"The result 7/12" -----> (5/8)n - 2/3 = 7/12
multiply each term by 24, the LCD
15n - 16 = 14
continue from here
5n/8-2/3=7/12
2.5n/4-2/3=7/12 multiply each side by 12
2.5*3n-8=7
7.5n=15
n=2
2 / 3 - n ∙ 5 / 8 = 7 / 12
2 / 3 - 5 n / 8 = 7 / 12
8 ∙ 2 / 8 ∙ 3 - 3 ∙ 5 n / 3 ∙ 8 = 2 ∙ 7 / 2 ∙ 12
16 / 24 - 15 n / 24 = 14 / 24
Subtract 16 / 24 to both sides
16 / 24 - 15 n / 24 - 16 / 24 = 14 / 24 - 16 / 24
- 15 n / 24 = - 2 / 24
Multiply both sides by 24
- 15 n = - 2
Divide both sides by - 15
n = - 2 / - 15
n = 2 / 15
To find the value of n, we need to reverse the operations that have been performed on it. Let's break it down step by step:
1. Start with a number, n.
2. Multiply n by 5/8: (5/8) * n = (5n)/8.
3. Subtract 2/3 from the result: (5n)/8 - 2/3 = 7/12.
To solve for n, we can follow these steps:
Step 1: Convert 7/12 into an equation with common denominators.
Multiply both sides of the equation by 12 to get rid of the denominator:
((5n)/8) * 12 - (2/3) * 12 = 7/12 * 12.
This simplifies to:
(5n * 3) - (2 * 4) = 7.
15n - 8 = 7.
Step 2: Isolate the variable.
Add 8 to both sides of the equation to get:
15n - 8 + 8 = 7 + 8.
This simplifies to:
15n = 15.
Step 3: Solve for the variable.
Divide both sides of the equation by 15 to get:
(15n)/15 = 15/15.
This simplifies to:
n = 1.
Therefore, the value of n is 1.