an electronics company makes two types of switches. type a takes 4 minutes to make and requires $3 worth of…

an electronics company makes two types of switches. type a takes 4 minutes to make and requires $3 worth of materials. type b takes 6 minutes to make and requires $6 of materials. in the latest production batch, it took 37 hours to make these switches, and the materials cost $2040. how many of each type of switch were made? there were type a switches and type b switches manufactured. (simplify your answers.)

an electronics company makes two types of switches. type a takes 4 minutes to make and requires $3 worth of materials. type b takes 6 minutes to make and requires $6 of materials. in the latest production batch, it took 37 hours to make these switches, and the materials cost $2040. how many of each type of switch were made? there were type a switches and type b switches manufactured. (simplify your answers.)

Answer

Explanation:

Step1: Set up equations

Let $x$ be the number of Type A switches and $y$ be the number of Type B switches. The time - related equation: Since Type A takes 4 minutes and Type B takes 6 minutes, and the total time is 37 hours (37×60 = 2220 minutes), we have $4x + 6y=2220$. Divide through by 2 to get $2x + 3y = 1110$. The cost - related equation: Since Type A requires $3 worth of materials and Type B requires $6 worth of materials, and the total material cost is $2040, we have $3x+6y = 2040$. Divide through by 3 to get $x + 2y=680$, which can be rewritten as $x=680 - 2y$.

Step2: Substitute $x$ into the first simplified equation

Substitute $x = 680-2y$ into $2x + 3y=1110$. $2(680 - 2y)+3y = 1110$. Expand: $1360-4y + 3y=1110$. Combine like terms: $1360 - y=1110$. Solve for $y$: $y=1360 - 1110=250$.

Step3: Find $x$

Substitute $y = 250$ into $x=680 - 2y$. $x=680-2\times250$. $x=680 - 500=180$.

Answer:

There were 180 Type A switches and 250 Type B switches manufactured.