A boutique owner sells a salt scrub that is made of a tropical oil blend costing $7.95 per ounce and sea salt costing $1.45 per ounce. The salt scrub ultimately costs $3.40 per ounce. In order to make a new batch of the salt scrub, she just ordered 6 ounces of the tropical oil blend. How many ounces of sea salt will she need to make the salt scrub with the correct proportions? Write your answer as a whole number or as a decimal rounded to the nearest tenth. ____ ounces

Question

A boutique owner sells a salt scrub that is made of a tropical oil blend costing $7.95 per ounce and sea salt costing $1.45 per ounce. The salt scrub ultimately costs $3.40 per ounce. In order to make a new batch of the salt scrub, she just ordered 6 ounces of the tropical oil blend. How many ounces of sea salt will she need to make the salt scrub with the correct proportions? Write your answer as a whole number or as a decimal rounded to the nearest tenth.   ____ ounces

Bytelearn · Accepted Answer

Calculate Total Cost: Let's denote the number of ounces of sea salt needed as 'x'. The total cost of the tropical oil blend for 6 ounces is 6 ounces * $7.95 per ounce. Calculate this value. 6 * $7.95 = $47.70Sea Salt Cost Expression: The total cost of the sea salt will be x ounces * $1.45 per ounce. Write this as an expression. Total cost of sea salt = x * $1.45Total Weight Expression: The total weight of the final salt scrub will be 6 ounces (tropical oil blend) + x ounces (sea salt). Write this as an expression. Total weight of salt scrub = 6 + x ouncesTotal Cost Equation: The total cost of the salt scrub per ounce is $3.40. The total cost of the salt scrub will be the cost per ounce times the total weight. Write this as an equation using the total weight expression from Step 3. Total cost of salt scrub = (6 + x) * $3.40Cost Equation Setup: The total cost of the salt scrub is the sum of the cost of the tropical oil blend and the cost of the sea salt. Set up an equation using the expressions from Step 1 and Step 2. $47.70 + (x * $1.45) = (6 + x) * $3.40Distribute and Solve: Distribute $3.40 on the right side of the equation to solve for x. $47.70 + (x * $1.45) = $20.40 + ($3.40 * x)Rearrange and Isolate: Rearrange the equation to isolate x on one side. $1.45x - $3.40x = $20.40 - $47.70Combine and Solve: Combine like terms and solve for x. -$1.95x = -$27.30 x = -$27.30 / -$1.95 x = 14

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