A company manufactures keyboards for desktop and laptop computers. The desktop keyboard contains 105 keys and the laptop keyboard has 90 keys. The company has 3000 keys and needs to produce twice as many desktop keyboards as laptop keyboards. How much of each type can the company produce?
Accepted Solution
A:
The company can produce 20 desktop keyboards and 10 laptop keyboardsStep-by-step explanation:A company manufactures keyboards for desktop and laptop computersThe desktop keyboard contains 105 keysThe laptop keyboard has 90 keysThe company has 3000 keysThe company needs to produce twice as many desktop keyboards as laptop keyboardsWe need to find how much of each type the company can produceAssume that the company can produce x desktop keyboards andy laptop keyboards∵ The company can produce x desktop keyboards∵ company can produce y laptop keyboards∵ The desktop keyboard contains 105 keys∵ The laptop keyboard has 90 keys∵ The company has 3000 keys- Write an equation to represent the total keys ∴ 105 x + 90 y = 3000 ⇒ (1)∵ The company needs to produce twice as many desktop keyboards as laptop keyboards∴ x = 2 y ⇒ (2)Substitute x in equation (1) by equation (2)∵ 105(2 y) + 90 y = 3000∴ 210 y + 90 y = 3000∴ 300 y = 3000- Divide both sides by 300∴ y = 10∴ The company can produce 10 laptop keyboardsSubstitute the value of y in equation (2) to find the value of x∵ x = 2(10)∴ x = 20∴ The company can produce 20 desktop keyboardsThe company can produce 20 desktop keyboards and 10 laptop keyboardsLearn more:You can learn more about the system of equations in brainly.com/question/2115716#LearnwithBrainly