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The equation below represents the amount of money left in Brianna’s pocket after buying donuts for her friends:
y = - 1.25x + 25
a)Explain what each value in the equation represents.
b)What is the greatest number of donuts Brianna can buy

Sagot :

  • y=-1.25x+25

Here rate of change is -1.25 (-ve) hence

  • x represents no of donuts
  • y represents price left

#b

The greatest no of donuts

  • -1.25x+25=0
  • -1.25x=-25
  • x=20donuts
semsee45

Answer:

Part (a)

Given equation:

[tex]y = - 1.25x + 25[/tex]

  • [tex]x[/tex] = number of donuts Brianna buys
  • [tex]y[/tex] = total amount of money in Brianna's pocket (in dollars)
  • [tex]-1.25[/tex] = For every donut Brianna buys, the money in her pocket decreases by $1.25 ⇒ each donut costs $.125
  • [tex]25[/tex] = Total amount of money Brianna has before she buys any donuts (in dollars) ⇒ $25.00

Part (b)

The greatest number of donuts Brianna can buy is when the money she has is reduced to zero dollars.  Therefore, substitute [tex]y = 0[/tex] into the equation and solve for [tex]x[/tex]:

[tex]\implies 0=-1.25x+25[/tex]

[tex]\implies 1.25x=25[/tex]

[tex]\implies x=\dfrac{25}{1.25}[/tex]

[tex]\implies x=20[/tex]

Therefore, the greatest number of donuts Brianna can buy is 20 donuts.

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