This week’s problems on reasoning with percents come from MathCounts Problem of the Week. Solutions can be found on the MathCounts site.
Tommy’s X-treme Smoothies
At Smoothies by Tommy, the X-treme Berry smoothie is made by combining four different kinds of fruit, sweetener and ice. Tommy has already added 14.4 oz of fruit and 1.2 oz of sweetener to the blender. If the X-treme Berry smoothie contains only fruit, sweetener and ice, how many ounces of ice does Tommy need to add to the blender to make an X-treme Berry smoothie, which is 35% ice?
Using the exact same amount of fruit and ice used in the X-treme Berry smoothie, Tommy creates the Xtreme Berry Lite smoothie by replacing the 1.2 oz of sweetener used in the X-treme Berry smoothie with an equal amount of zero-calorie sugar alternative. The 14.4-oz fruit mixture, which accounts for 100% of the calories in the X-treme Berry Lite smoothie, accounts for only 70% of the calories in the Xtreme Berry smoothie. If there are 280 calories in the X-treme Berry Lite smoothie, how many calories are in 1 oz of the sweetener used to make the X-treme Berry smoothie?
The X-treme Berry smoothie costs $5.00. Customers who want a boost of energy can order the Super Xtreme Berry smoothie. There is an additional charge of 75 cents to turn an X-treme Berry smoothie into a Super X-treme Berry smoothie by having a protein supplement added. Paula placed an order for 5 smoothies and paid $27.25, not including tax. If Paula’s order contained both X-treme Berry and Super X-treme Berry smoothies, what is the positive difference in the total amount she paid for the Xtreme Berry smoothies and the total amount she paid for the Super Xtreme Berry smoothies?