Question

directions: show all work in order to receive full credit. remember to identify the solution. 1. a school buys 15 calculators and 10 rulers for $350. another school buys 8 calculators and 6 rulers for $184. what is the cost of one calculator and one ruler? (15x + 10 = 350; 8x + 6 = 184) y = 012rs

Explanation:

Step1: Define variables

Let $x$ = cost of 1 calculator, $y$ = cost of 1 ruler.

Step2: Set up system of equations

$$\begin{cases} 15x + 10y = 350 \\ 8x + 6y = 184 \end{cases}$$

Step3: Simplify first equation

Divide by 5: $3x + 2y = 70$

Step4: Isolate $2y$ in simplified eq

$2y = 70 - 3x$

Step5: Simplify second equation

Divide by 2: $4x + 3y = 92$

Step6: Substitute $2y$ into second eq

Replace $3y$ with $\frac{3}{2}(70-3x)$:
$4x + \frac{3}{2}(70-3x) = 92$
Multiply all terms by 2: $8x + 210 - 9x = 184$

Step7: Solve for $x$

$-x = 184 - 210$
$-x = -26$
$x = 26$

Step8: Solve for $y$

Substitute $x=26$ into $2y=70-3x$:
$2y = 70 - 3(26)$
$2y = 70 - 78$
$2y = -8$
$y = 4$

Answer:

The cost of one calculator is $\$26$, and the cost of one ruler is $\$4$.