A markup, discount, and tax form a chain of successive percent changes. Start with the missing wholesale cost, use one multiplier for each change, and solve the resulting equation with a Desmos regression. Each percent acts on the price left by the previous change. The trap is treating the discount and tax as if both used the regular price.
Hints
- Hint 1
A markup adds to the price it starts with. A markup keeps the whole wholesale cost and adds half of it. What multiplier gives the regular selling price?
- Hint 2
A discount removes part of the current price. The off applies to the regular selling price, not the wholesale cost. What percent of the regular price remains?
- Hint 3
Sales tax is added after the discount. The tax is calculated from the discounted price, so what multiplier turns that price into the checkout total?
Step-by-step
Chain the price changes, then solve
Step 1Write the regular price
Let be the wholesale cost in dollars. A markup adds half of that cost to the whole cost, so the regular selling price is:
- Step 2
Write the discounted price
The discount leaves of the regular price, . So the sale price is:
Don't take off : the sale is advertised off the regular selling price.
- Step 3
Connect the total to the wholesale cost
The sales tax makes the checkout total of the discounted price. The customer pays $59.40, so:
- Step 4
Solve for the wholesale cost
Type in Desmos, with standing for . Use instead of the graphing variable , and use instead of so Desmos fits the unknown. Under PARAMETERS, it shows . The wholesale cost was $45. Grid in 45.