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?

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?

Answer

Explanation:

Step1: Define variables

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

Step2: Set up total quantity equation

Total t-shirts sold: $x + y = 30$

Step3: Set up total revenue equation

Total money made: $10x + 15y = 380$

Step4: Isolate variable from first equation

Rearrange $x + y = 30$ to $x = 30 - y$

Step5: Substitute into revenue equation

Substitute $x = 30 - y$ into $10x + 15y = 380$: $10(30 - y) + 15y = 380$ $300 - 10y + 15y = 380$ $300 + 5y = 380$

Step6: Solve for $y$

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

Step7: Solve for $x$

Substitute $y=16$ into $x = 30 - y$: $x = 30 - 16 = 14$

Answer:

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

Completed Table:

CLAIM EVIDENCE REASONING
14 plain t-shirts and 16 printed t-shirts were sold. Plain t-shirts: $10 each, printed: $15 each; 30 total t-shirts sold, $380 total revenue. Define variables for each t-shirt type, set up system of equations for total quantity and revenue, substitute to solve for one variable, then find the second variable. Verify: $10(14) + 15(16) = 140 + 240 = 380$, and $14+16=30$, which matches the given totals.