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Solution: Let the number of mackerel be $ m $. The ratio $ 5:4 = 20:m $ implies $ \frac{5}{4} = \frac{20}{m} $. Cross-multiplying: $ 5m = 80 $ → $ m = 16 $. There are $ \boxed{16} $ mackerel.
Question: Solve for $ y $ in the equation $ \frac{3y - 1}{4} = \frac{y + 7}{2} $.
Solution: Cross-multiply: $ 2(3y - 1) = 4(y + 7) $. Expand: $ 6y - 2 = 4y + 28 $. Subtract $ 4y $: $ 2y - 2 = 28 $. Add 2: $ 2y = 30 $. Divide by 2: $ y = 15 $. Final answer: $ \boxed{15} $.
Question: What is the arithmetic mean of the numbers 14, 19, and 23?
Solution: The arithmetic mean is $ \frac{14 + 19 + 23}{3} = \frac{56}{3} $. Simplifying, the mean is $ \boxed{\dfrac{56}{3}} $.### Question 1
A company produces two types of widgets, Type A and Type B. Type A widgets take 3 hours to produce, and Type B widgets take 5 hours. In one day, the company produces a total of 20 widgets, spending exactly 80 hours in production. How many Type A and Type B widgets does the company produce?
Let \( x \) be the number of Type A widgets and \( y \) be the number of Type B widgets. We have the system of equations:
\( x + y = 20 \)
\( 3x + 5y = 80 \)
From equation 1, express \( y \) in terms of \( x \):