Respuesta :
Answer:
The quantity of first mixture = x = 75 pounds
The quantity of second mixture = 175 - x = 175 - 75 = 100 pounds
Step-by-step explanation:
Total quantity of mixture = 175 pounds
Let quantity of first mixture = x
Quantity of second mixture = 175 - x
From the given information
x (0.9) + (175 - x) × 1.6 = 175 × 1.3
By solving above equation we get
0.9 x + 280 - 1.6 x = 227.5
0.7 x = 52.5
x = 75 pounds
Thus the quantity of first mixture = x = 75 pounds
The quantity of second mixture = 175 - x = 175 - 75 = 100 pounds
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 [tex]\times[/tex] 90 = $0.9
Let quantity of nut A mixed = [tex]x\ pound[/tex]
Quantity of nut B mixed = [tex]175-x\ pound[/tex]
Total quantity of mixture = 175 pounds
Total cost of mixture = Cost per pound [tex]\times[/tex] Total quantity of mixture in pound
= $1.30 [tex]\times[/tex] 175 = $227.5
As mixture is prepared by mixing two types of nuts:-
Cost per pound of nut A [tex]\times[/tex] Quantity mixed + Cost per pound of nut B
[tex]0.9x+1.60(175-x)=227.5\\0.9x+280-1.60x=227.5\\-0.7x+280=227.5\\[/tex]
By subtracting both sides by 280
[tex]-0.7x=-52.5[/tex]
Minus canceled by minus
[tex]0.7x=52.5\\Dividing\ both\ sides\ by\ 0.7\\x=75\ pound[/tex]
Substituting the value:-
Quantity of nut A mixed = [tex]x\ pound[/tex] = 75 pounds
Quantity of nut B mixed = [tex]175-x\ pound[/tex]= 175 - 75 = 100 pounds
Therefore, Bons grocer wishes to mix 75 pounds of nuts worth 90 cents ($0.9) with 100 pounds of some nuts worth $1.60 per pound to make 175 pounds of a mixture that is worth $1.30 per pound.
