Question

(3 9/16-y)+4 9/14=5 7/16 решите уравнение

Answer 1

Вот решение уравнения

Answer 2

To solve the equation (3 9/16 - y) + 4 9/14 = 5 7/16, we need to find the value of y. First, we'll simplify the left side of the equation:

Step 1: Convert the mixed numbers to improper fractions. 3 9/16 = (3 * 16 + 9) / 16 = 57/16 4 9/14 = (4 * 14 + 9) / 14 = 65/14

Step 2: Rewrite the equation using improper fractions. (57/16 - y) + 65/14 = 87/16

Step 3: Find a common denominator for the fractions (16 and 14 share a common multiple, which is 112). To convert 57/16 to have a denominator of 112, multiply both the numerator and denominator by 7. 57/16 * 7/7 = 399/112

To convert 65/14 to have a denominator of 112, multiply both the numerator and denominator by 8. 65/14 * 8/8 = 520/112

The equation becomes: (399/112 - y) + 520/112 = 87/16

Step 4: Combine the fractions on the left side of the equation. (399/112 - y + 520/112) = 87/16

Step 5: Simplify the left side further. (399 + 520 - 112y) / 112 = 87/16

Step 6: Combine the constant terms on the left side. (919 - 112y) / 112 = 87/16

Step 7: Cross-multiply to eliminate the fraction. 87 * 112 = 16 * (919 - 112y)

Step 8: Solve for y. 9804 = 14704 - 1792y

Step 9: Move the variable terms to one side of the equation. 1792y = 14704 - 9804

Step 10: Perform the subtraction. 1792y = 4900

Step 11: Solve for y by dividing both sides by 1792. y = 4900 / 1792

Step 12: Find the decimal approximation for y. y ≈ 2.7356

So, the value of y that satisfies the equation is approximately 2.7356.