G.O has 3 orange picks for every 2 green. If there are 25 picks in all, how many picks are orange?
1 answer:
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Answer:
Amanda buy first kind of pen = 3
Amanda buy second kind of pen = 2
Amanda buy third kind of pen = 15
Step-by-step explanation:
Given - Amanda went to the store to purchase ink pens. She found three
kinds of pens. The first cost $4 each; the price of the second kind
was 4 for $1; and the cost for the third kind was 2 for $1. She bought
20 pens and she bought at least one of each kind. (It is possible to
buy only 1 of the pens that are "4 for $1" or "2 for $1".) The cost was
$20.
To find - When she got back to her office, Amanda decided to turn this into
a math problem for me. She asked: how many of each kind did I
buy?
Proof -
Let Amanda buy first kind of pen = x
second kind of pen = y
third kind of pen = z
As given,
She bought total pen = 20
⇒x + y + z = 20 ...............(1)
Now,
As given,
cost for first kind pen = $4 for 1 pen
As she bought x pens of first kind , so
Cost of x pens of first kind = $4x
Now,
The price of the second kind was 4 for $1
⇒Cost of second kind = $ for 1 pen
As she bought y pens of send kind , so
Cost of y pens of second kind = $
Now,
The price of the third kind was 2 for $1
⇒Cost of third kind = $ for 1 pen
As she bought z pens of send kind , so
Cost of z pens of third kind = $
Now,
As given, The cost was $20
⇒4x + +
= 20
⇒16x + y + 2z = 80 .....................(2)
∴ we get 2 equations
x + y + z = 20 .....................(1)
16x + y + 2z = 80 .....................(2)
Now,
Subtract equation (1) from equation (2) , we get
16x + y + 2z - ( x+ y + z )= 80 - 20
⇒16x + y + 2z - x - y - z = 60
⇒15x + z = 60
⇒z = 60 - 15x
Now,
Put the value of z in equation (1) , we get
x + y + 60 - 15 x = 20
⇒ y - 14x = 20 - 60
⇒y - 14x = -40
⇒14x - y = 40
⇒y = 14x - 40
Now,
we get
z = 60 - 15x
y = 14x - 40
As given
she bought at least one of each kind
it means x > 1, y > 1, z > 1
Now,
If x = 1, then y = 14 - 40 = -26
Not possible
If x = 2 , then y = 14(2) - 40 = -12
Not possible
If x = 3, then y = 14(3) - 40 = 2 and z = 60 - 15(3) = 15
Possible.
If x = 4, then y = 14(4) - 40 = 16 and z = 60 - 15(4) = 0
Not Possible.
If x = 5, then y = 14(5) - 40 = 30 and z = 60 - 15(5) = -15
Not Possible.
∴ we get
x = 3, y = 2, z = 15
Amanda buy first kind of pen = x = 3
Amanda buy second kind of pen = y = 2
Amanda buy third kind of pen = z = 15
Answer:
x ∈ {-5, -1}
Step-by-step explanation:
Here's the solution using the quadratic formula:
The real zeros are -5 and -1.
_____
There are many ways to check your answer. One of them is to look at the given quadratic, which has no changes of sign in its coefficients. (They are all positive.) That means there can be no positive real roots, so already you know that x=0.5 won't work.
Also, the constant in the quadratic is the product of the roots, For your roots, their product is -7/4, so even multiplying by 4 (the leading coefficient in the given quadratic), you don't get anything like 20.
