Question

Рівняння 8 7/9 - X = 3 5/6 До магазину завезли фрукти. Яблука складали 1/4 сливи 3/10 а груші 5/12 всіх завезених фруктів решту завезеного товару становив виноград. Яку частину фруктів становив виноград

Answer 1

Equation Solution

The equation 8 7/9 - x = 3 5/6 can be solved by first converting the mixed numbers to improper fractions and then isolating the variable x.

Converting the mixed numbers to improper fractions: - 8 7/9 = (8 * 9 + 7)/9 = 71/9 - 3 5/6 = (3 * 6 + 5)/6 = 23/6

So, the equation becomes: 71/9 - x = 23/6

To solve for x: - Subtract 71/9 from both sides: -x = 23/6 - 71/9 - Find a common denominator for 6 and 9, which is 18: -x = (23*3)/(6*3) - (71*2)/(9*2) = 69/18 - 142/18 - Combine the fractions: -x = (69 - 142)/18 = -73/18 - Multiply both sides by -1 to solve for x: x = 73/18

Proportion of Grapes

The proportion of grapes in the delivered fruits can be calculated based on the information provided.

Given: - Apples: 1/4 - Plums: 3/10 - Pears: 5/12

To find the proportion of grapes, we need to subtract the sum of the proportions of apples, plums, and pears from 1 (since the total proportion of all fruits is 1).

Calculating the sum of the proportions of apples, plums, and pears: - 1/4 + 3/10 + 5/12 = 15/60 + 18/60 + 25/60 = 58/60

Subtracting the sum from 1 to find the proportion of grapes: - 1 - 58/60 = 60/60 - 58/60 = 2/60 = 1/30

Therefore, the proportion of grapes in the delivered fruits is 1/30.