Question

learning target: i can solve real - world problems algebraically and graphically with systems of equations. (2 pts) caysen and kyle are selling t - shirts and sweatshirts with the school logo. caysen sells 6 t - shirts and 4 sweatshirts for $212. kyle sells 3 t - shirts and 5 sweatshirts for $202. part a write a system of equations to represent the situation. using x for the price of t - shirts and y for the price of sweatshirts. caysen: blank kyle: blank part b solve the system of equations using elimination or substitution. show your work. x = blank y = blank part c what does the solution of the system mean in this situation?

Explanation:

Step1: Form equations for Part A

Caysen sells 6 T - shirts and 4 sweatshirts for $212, so the equation is $6x + 4y=212$. Kyle sells 3 T - shirts and 5 sweatshirts for $202, so the equation is $3x + 5y=202$.

Step2: Solve the system for Part B (using elimination)

Multiply the second equation $3x + 5y=202$ by 2 to get $6x+10y = 404$. Now subtract the first equation $6x + 4y=212$ from it.
$(6x + 10y)-(6x + 4y)=404 - 212$.
$6x+10y - 6x - 4y=192$.
$6y=192$, then $y=\frac{192}{6}=32$.
Substitute $y = 32$ into the first equation $6x+4\times32 = 212$.
$6x+128 = 212$.
$6x=212 - 128=84$.
$x=\frac{84}{6}=14$.

Step3: Interpret the solution for Part C

The value of $x = 14$ means the price of each T - shirt is $14. The value of $y = 32$ means the price of each sweatshirt is $32.

Answer:

Part A:
Caysen: $6x + 4y=212$
Kyle: $3x + 5y=202$
Part B:
$x = 14$
$y = 32$
Part C: The price of a T - shirt is $14 and the price of a sweatshirt is $32.