a clothing store sells two types of t-shirts: plain and printed. plain t-shirts cost $10 each, and printed…

a clothing store sells two types of t-shirts: plain and printed. plain t-shirts cost $10 each, and printed t-shirts cost $15 each. the store sold a total of 30 t-shirts and made $380. how many plain and how many printed t-shirts were sold?\nclaim\n14 plain t-shirts and 16 printed t-shirts were sold.\nevidence\nplain shirts $10 each, printed shirts $15 each\n30 total shirts sold.\nreasoning

a clothing store sells two types of t-shirts: plain and printed. plain t-shirts cost $10 each, and printed t-shirts cost $15 each. the store sold a total of 30 t-shirts and made $380. how many plain and how many printed t-shirts were sold?\nclaim\n14 plain t-shirts and 16 printed t-shirts were sold.\nevidence\nplain shirts $10 each, printed shirts $15 each\n30 total shirts sold.\nreasoning

Answer

Explanation:

Step1: Define variables

Let $x$ = number of plain t-shirts, $y$ = number of printed t-shirts.

Step2: Set up total quantity equation

$x + y = 30$

Step3: Set up total revenue equation

$10x + 15y = 380$

Step4: Isolate $x$ from Step2

$x = 30 - y$

Step5: Substitute $x$ into Step3 equation

$10(30 - y) + 15y = 380$ $300 - 10y + 15y = 380$ $300 + 5y = 380$

Step6: Solve for $y$

$5y = 380 - 300$ $5y = 80$ $y = \frac{80}{5} = 16$

Step7: Solve for $x$ using $y=16$

$x = 30 - 16 = 14$

Answer:

14 plain t-shirts and 16 printed t-shirts were sold.