Atte Mia

24. Critical Thinking Anika wants to determine the maximum

number of tulip bulbs (t) she can purchase if each bulb costs $1.50.

She will also need to purchase separate pots for each bulb at $1.25

each and a bag of potting soil for $10.00. Set up an inequality to

determine how many tulip bulbs Anika can purchase without

spending more than $20.00, and solve it. Can Anika buy exactly

enough bulbs and pots to spend the full $20.00? Explain. Can you

think of a better inequality to describe the answer?

Noti

My

C

25. Geometry The area of the triangle shown is no more than 10 square inches.

a. Write an inequality that can be used to find x.

Copy

(2x - 3) in.

4 in.

b. Solve the inequality from part a.

What is the maximum height of the triangle?

Klein

Tanis

Kindly check explanation

Step-by-step explanation:

Given the following :

Cost per bulb = $1.50

Cost per pot = $1.25

Bag of potting soil = $10.00

Budgeted amount to spend ≤ 20

Cost :

Bag of potting soil + (Cost per bulb + cost per pot)*number of tulip bulbs ≤ 20

$10 + ($1.50 + $1.25)t ≤ $20

$10 + 2.75t ≤ 20

$2.75t ≤ $20 - $10

$2.75t ≤ $10

t ≤ $10/$2.75

t ≤ 3.636

Hence, t = maximum number of tulip bulbs she can purchase is 3.636,

Since the exact number of tulip bulb she can purchase is a decimal which is impossible in an actual scenario. Hence, In other to spend not more than $20.00

t ≤ 3

step-by-step explanation:

30% of $420 is 0.30($420) = $126 and $420 + $126 = $546.

or, 130% of $420 is 1.3($420) = $546.

notice that this is not the $600 original list price with which we started.

why doesn't this work?

the method does not work because 30% of $420 is not the same amount as the 30% of $600. it may seem obvious when stated this way, but it is a very common error made on problems of this type. we cannot just use the same percent and get back to the original amount because we are taking that percent of a different value.

to work problems of this type correctly, it is generally best to write an equation for the situation and then solve.

example: since (100% – 30%)(original price) = (sale price)

70% of the   (original price) is $420.

0.7x   = 420

equation image indicator

x = 600

the original cost was $600.

we may also solve this problem using the two-step method. working the problem in two steps requires us to use more algebra skills. we have to know that x = 1x (identity property of multiplicationtext annotation indicator) and that 1x – 0.3x = 0.7x (subtracting like terms). then we solve the problem as follows:

(original price) – 30%(original price) = sale price

x – 0.3x = 420

0.7x = $420

equation image indicator

x = 600

the original cost was $600.  

note that with both of the above methods we do obtain the correct original amount.

example: after a 5% pay raise, hermione is earning $22,680 per year. what was she earning before the pay raise?

105% of (original salary) = current salary

1.05x = 22,680

equation image indicator

x = 21,600

hermione earned $21,600 per year before the pay raise.

this is an example so maybe you will get how to at least do it!

2x^2+5x+17

your welcome. : )