6. Bons grocer wishes to mix some nuts worth 90 cents per pound with some nuts worth $1.60 per pound to make 175 pounds of a mix
2 answers:
Answer:
75 pounds and 100 pounds.
Step-by-step explanation:
Given:
Bons grocer wishes to mix some nuts worth 90 cents( $0.9) per pound with some nuts worth $1.60 per pound to make 175 pounds of a mixture that is worth $1.30 per pound.
Question asked:
How much of each should she use?
Solution:
Let there are two types of nuts mixed in the mixture, one is nut A and another is nut B.
As we know:
1 cent = $0.01
90 cents = $0.01 90 = $0.9
Let quantity of nut A mixed =
Quantity of nut B mixed =
Total quantity of mixture = 175 pounds
Total cost of mixture = Cost per pound Total quantity of mixture in pound
= $1.30 175 = $227.5
As mixture is prepared by mixing two types of nuts:-
Cost per pound of nut A Quantity mixed + Cost per pound of nut B
By subtracting both sides by 280
Minus canceled by minus
Substituting the value:-
Quantity of nut A mixed = = 75 pounds
Quantity of nut B mixed = = 175 - 75 = 100 pounds
Therefore, Bons grocer wishes to mix<u> 75 pounds of nuts worth 90 cents</u> ($0.9) with <u>100 pounds of some nuts worth $1.60 </u>per pound to make 175 pounds of a mixture that is worth $1.30 per pound.
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Answer:
YES
NO
NO
Step-by-step explanation:
The given polynomial is:
(x - a) is a factor of a polynomial iff x = a is a solution to the polynomial.
To check if (x - 5) is a factor of the polynomial f(x), we substitute x = 5 and check if it satisfies the equation.
∴ f(5) = 5³ + 4(5)² - 25(5) - 100
= 125 + 100 - 125 - 100
= 225 - 225
= 0
We see, x = 5 satisfies f(x). So, (x - 5) is a factor to the polynomial.
Now, to check (x + 2) is a factor.
i.e., to check x = - 2 satisfies f(x) or not.
f(-2) = (-2)³ + 4(-2)² - 25(-2) - 100
= -8 + 16 + 50 - 100
= -108 + 66
≠ 0
Therefore, (x + 2) is not a factor of f(x).
To check (x - 4) is a factor.
∴ f(4) = 4³ + 4(4)² - 25(4) - 100
= 64 + 64 - 100 - 100
= 128 - 200
≠ 0
Therefore, (x - 4) is not a factor of f(x).