1963 TMTA High School Algebra I Contest Problem 38

Problem

A farmer sold $60$ hogs for $$2030.$ Some were sold for $$ 30$ , and the remainder were sold for $$ 40$ each. How many were sold at $$ 30$ each?

$\text{(A)} \quad 37; \quad \text{(B)} \quad 19; \quad \text{(C)} \quad 29; \quad \text{(D)} \quad 42; \quad \text{(E)} \quad \text{none of these}$

Solution

If there were $h$ hogs sold at $30$ dollars each, then there were $60-h$ hogs sold at $40$ dollars each. Using this, we can construct an equation which lets us solve for $h$ , the number of hogs sold at $30$ dollars each.

$30h + 40(60-h) = 2030$ $30h - 40h + 2400 = 2030$ $-10h = -370$ $h = \frac{-370}{-10} = 37.$

The answer is $\boxed{\text{(A)}}$ .

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1963 TMTA High School Algebra I Contest Problem 38

Problem

Solution