Application Problems

Ratios

Example Problem: A recipe requires 3 cups of flour for every 2 cups of sugar. If you want to make a batch using 9 cups of flour, how many cups of sugar do you need?

Solution: Set up the ratio: \(\frac{3 \text{ cups flour}}{2 \text{ cups sugar}} = \frac{9 \text{ cups flour}}{x \text{ cups sugar}}\)

Cross-multiply and solve for ( x ): \(3x = 18 \implies x = 6\)

You need 6 cups of sugar.

Proportions

Example Problem: If a car travels 150 miles in 3 hours, how far will it travel in 5 hours at the same speed?

Solution: Set up the proportion: \(\frac{150 \text{ miles}}{3 \text{ hours}} = \frac{x \text{ miles}}{5 \text{ hours}}\)

Cross-multiply and solve for ( x ): \(3x = 750 \implies x = 250\)

The car will travel 250 miles in 5 hours.

Percents

Example Problem: A store is having a 25% off sale on a jacket that originally costs $80. What is the sale price of the jacket?

Solution: Calculate 25% of $80: \(0.25 \times 80 = 20\)

Subtract the discount from the original price: \(80 - 20 = 60\)

The sale price of the jacket is $60.

Linear Equations with One Unknown

Example Problem: Solve for ( x ): ( 2x + 5 = 17 )

Solution: Subtract 5 from both sides: \(2x = 12\)

Divide both sides by 2: \(x = 6\)

The solution is ( x = 6 ).

Practice Questions

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