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Brix and his family have a family business of making tiny pots for both "plantitos" and "plantitas". An order of no less than 160 pots of both designs, cube and cylindrical, from Mr. Dagohoy is accepted by the family. The cube design has a price tag of Php 70.00 each, while the cylindrical design is Php 50.00 each. Mr. Dagohoy expects a price range of around Php 9.500.00 to Php 13, 000.00. How many pots of each design will the amount he expects be produced? Provide 2 possible combinations of the number of pots of each design.

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Nonsense will been Autoreported, please donot waste my points. Please help me. ​

Sagot :

let the number of cubes be x the number of cylindrical be y

9 500 <_ 70 x 150y <_ 13000

xty 2160

so they can buy

80 cubes

80 cylindricals

or

60 cubes

120 cylindricals

i tried :)

MayumeLovesModulesidn

✏️Linear Inequalities in Two Variables

[tex] \red{⊱─━━━━━━━━⊱༻●༺⊰━━━━━━━━─⊰}\: [/tex]

[tex] \large\mathbb\red{PROBLEM:} \: [/tex]

Brix and his family have a family business of making tiny pots for both "plantitos" and "plantitas". An order of no less than 160 pots of both designs, cube and cylindrical, from Mr. Dagohoy is accepted by the family. The cube design has a price tag of Php 70.00 each, while the cylindrical design is Php 50.00 each. Mr. Dagohoy expects a price range of around Php 9.500.00 to Php 13, 000.00. How many pots of each design will the amount he expects be produced? Provide 2 possible combinations of the number of pots of each design.

[tex] \red{⊱─━━━━━━━━⊱༻●༺⊰━━━━━━━━─⊰}\: [/tex]

[tex] \large\mathbb\red{SOLUTION:} \: [/tex]

Step 1: Understand the problem. Represent the unknown.

Let:

  • x = the number of cube designs.
  • y = the number of cylindrical designs.

Step 2: Devise a plan. Translate or write the inequality.

  • [tex] \small \sf{x + y > 160}[/tex]
  • [tex] \small \sf{70x + 50y \geqslant 9500}[/tex]

Step 3: Carry out the plan. Solve the inequality. Use intercept method this time, then graph.

Solving for x-intercept. Let y = 0.

  • x + y > 160 ⇛ x + y = 160 ⇛y = 160 - x
  • 70x + 50y = 9500
  • 70x + 50(160-x) = 9500
  • 70x + 8000 - 50x = 9500
  • 70x -50x = 9500 - 8000
  • 20x = 1500
  • x = 75

Solving for y-intercept. Let x = 0

  • 70x + 50y = 9500
  • 70(75) + 50y = 9500
  • 5250 + 50y = 9500
  • 50y = 9500 - 5250
  • 50y = 4250
  • y = 85

Hence, the number of the cube designs is at least 75 pieces, while the number of cylindrical design is at least 85 pieces.

Step 4: Look back. Check your solution then interpret the result.

Now, we choose 2 possible combinations of the number of pots of each design. Let us use (80,100) and (60,140). Substitute each point in the inequality.

A. (80,100)

  • [tex] \small\sf{70x + 50y \geqslant 9500}[/tex]
  • [tex]\small\sf{70(80) + 50(100) \geqslant 9500} \: [/tex]
  • [tex]\small\sf{5600+ 5000 \geqslant 9500} \: [/tex]
  • [tex]\small\sf{10,600 \geqslant 9500} \: - TRUE[/tex]

B. (60,140)

  • [tex]\small\sf{70x + 50y \geqslant 9500} \: [/tex]
  • [tex]\small\sf{70(60) + 50(140) \geqslant 9500}[/tex]
  • [tex] \small \sf{4200 + 7000 \geqslant 9500}[/tex]
  • [tex] \small \sf{11,200 \geqslant 9500 - TRUE}[/tex]

[tex] \red{⊱─━━━━━━━━⊱༻●༺⊰━━━━━━━━─⊰}\: [/tex]

[tex]\large\mathbb\red{ANSWER:} \: [/tex]

Therefore, Brix and his family can sell at least 75 pieces of cube designs and 85 pieces of cylindrical designs to achieve their desired amount of at least P 9500.00.

[tex]\red{⊱─━━━━━━━━⊱༻●༺⊰━━━━━━━━─⊰} \: [/tex]

[tex] \tiny{\color{red}{\boxed{\colorbox{pink}{\color{red}{\tiny{❁{\color{red}{\tiny{\:Carry On Learning}{\color{red} {\tiny{❁}}}}}}}}}}} \tiny\red{-Mayume}\: [/tex]

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