13. three types of apples are sold at the market, fuji, gala, and honeycrisp. the sales profit is the same…

13. three types of apples are sold at the market, fuji, gala, and honeycrisp. the sales profit is the same for each, $2.50. one week in june, the number of fuji apples sold was four less than twice the number of gala apples. fifteen more honeycrisp apples were sold than gala apples. combined, a total of 479 apples were sold. how much money did the market make from the sale of each type of apple that week?

13. three types of apples are sold at the market, fuji, gala, and honeycrisp. the sales profit is the same for each, $2.50. one week in june, the number of fuji apples sold was four less than twice the number of gala apples. fifteen more honeycrisp apples were sold than gala apples. combined, a total of 479 apples were sold. how much money did the market make from the sale of each type of apple that week?

Answer

Explanation:

Step1: Define variables

Let the number of Gala apples be $x$. Then the number of Fuji apples is $2x - 4$, and the number of Honeycrisp apples is $x + 15$.

Step2: Set up an equation

The total number of apples sold is 479. So, $(2x - 4)+x+(x + 15)=479$.

Step3: Simplify the left - hand side of the equation

Combine like terms: $2x-4+x+x + 15=4x+11$. So, $4x + 11=479$.

Step4: Solve for $x$

Subtract 11 from both sides: $4x=479 - 11=468$. Then divide both sides by 4: $x=\frac{468}{4}=117$.

Step5: Find the number of each type of apple

Number of Gala apples: $x = 117$. Number of Fuji apples: $2x-4=2\times117 - 4=234 - 4=230$. Number of Honeycrisp apples: $x + 15=117+15=132$.

Step6: Calculate the profit for each type of apple

Since the profit per apple is $2.50. Profit from Gala apples: $2.50\times117 = 292.5$. Profit from Fuji apples: $2.50\times230=575$. Profit from Honeycrisp apples: $2.50\times132 = 330$.

Answer:

Profit from Gala apples: $$292.5$, Profit from Fuji apples: $$575$, Profit from Honeycrisp apples: $$330$