Question

1. gaia saw that a blender was discounted 35% from its original price of $39.99. what is the discounted price of the blender? explain your thinking.
2. due to bad weather, there is a shortage of pumpkins this year. a company normally sells its cans of pumpkin pie mix for $2.88 but needs to add a 17% markup to make up for losses. what is the new price of a can of pumpkin pie mix?
3. rashon has a coupon that discounts the price of a night of laser tag by 28%. it will now cost him and his friends $45 to play laser tag for one night. what is the original price of playing laser tag?
4. lena took her cat to a groomer for a bath and brushing, which costs $50. because her cats fur was very knotted, lena decided to give the groomer a 20% tip. what was the final price of the grooming?
5. cosmo needed to take a week off from his summer job to go on vacation. this meant he received a 17% cut in his pay for the week. his paycheck for that week was $265.60. what does he normally make in a week?
6. at the end of the year, ms. omeara earned a 13% bonus at work. if her annual salary is $76,450, what was her salary with the bonus?

Explanation:

Step1: Calculate the discount amount

The discount rate is \(35\% = 0.35\). The original price of the blender is \(P = 39.99\). The discount amount \(D\) is given by the formula \(D=P\times r\), where \(r\) is the discount rate. So \(D = 39.99\times0.35=13.9965\approx14.00\)

Step2: Calculate the discounted price

The discounted price \(DP\) is the original price minus the discount amount. Using the formula \(DP = P - D\), we substitute \(P = 39.99\) and \(D\approx14.00\). So \(DP=39.99 - 14.00 = 25.99\)

Step1: Calculate the markup amount

The markup rate is \(17\%=0.17\). The original price of the pumpkin - pie mix is \(P = 2.88\). The markup amount \(M\) is given by the formula \(M = P\times r\), where \(r\) is the markup rate. So \(M=2.88\times0.17 = 0.4896\approx0.49\)

Step2: Calculate the new price

The new price \(NP\) is the original price plus the markup amount. Using the formula \(NP=P + M\), we substitute \(P = 2.88\) and \(M\approx0.49\). So \(NP=2.88+0.49 = 3.37\)

Step1: Set up the equation

Let the original price be \(x\). The discount rate is \(28\% = 0.28\), so the price after discount is \((1 - 0.28)x=0.72x\). We know that \(0.72x = 45\)

Step2: Solve for \(x\)

Using the formula \(x=\frac{45}{0.72}\). We calculate \(\frac{45}{0.72}=\frac{4500}{72}=62.5\)

Step1: Calculate the tip amount

The tip rate is \(20\%=0.2\). The cost of grooming is \(C = 50\). The tip amount \(T\) is given by the formula \(T = C\times r\), where \(r\) is the tip rate. So \(T=50\times0.2 = 10\)

Step2: Calculate the final price

The final price \(FP\) is the cost of grooming plus the tip amount. Using the formula \(FP=C + T\), we substitute \(C = 50\) and \(T = 10\). So \(FP=50 + 10=60\)

Answer:

The discounted price of the blender is \(\$25.99\)