A number, plus one third itself, plus one eighth of itself, equals 70. What is the number?
Let's solve the equation step-by-step.
Let's assume the number is x.
According to the information given, the equation can be written as:
x + 1/3 * x + 1/8 * x = 70
Let's simplify each term:
8/8 * x + 3/8 * x + 1/8 * x = 70
Combining the terms with the same denominator,
(8x + 3x + x) / 8 = 70
12x / 8 = 70
Multiplying both sides of the equation by 8 to eliminate the fraction,
12x = 8 * 70
12x = 560
Next, we can solve for x by dividing both sides of the equation by 12:
x = 560 / 12
x = 46.67
Therefore, the number is approximately 46.67.
To solve this problem, we need to set up an equation based on the given information. Let's call the unknown number "x". According to the problem, the number plus one third of itself (1/3x) plus one eighth of itself (1/8x) equals 70.
So the equation would be:
x + 1/3x + 1/8x = 70
To simplify this equation, we need to find a common denominator for the fractions. The least common multiple of 3 and 8 is 24. Multiplying each term by 24, we get:
24x + 8(1/3x) + 3(1/8x) = 24(70)
Simplifying further, we have:
24x + 8/3x + 3/8x = 1680
To add the fractions, we need a common denominator of 24. Multiplying each fraction by appropriate factors, we get:
24x + (64/24)x + (9/24)x = 1680
Simplifying, we have:
24x + 64x/24 + 9x/24 = 1680
Combining the like terms, we have:
(72x + 64x + 9x)/24 = 1680
Simplifying the numerator, we get:
(145x)/24 = 1680
To isolate "x", we multiply both sides of the equation by 24/145:
x = (24/145) * 1680
Evaluating the right side of the equation, we have:
x = 28
Therefore, the number is 28.
x + (1/3)x + (1/8)x = 70
x + 0.333x + 0.125x = 70
1.458x = 70
x = 48