Respuesta :
Answer:
[tex]7.5\text{ lbs and }5\text{ lbs}[/tex]
Step-by-step explanation:
GIVEN: You have one type of nut that sells for [tex]\$2.80\text{/lb}[/tex] and another type of nut that sells for [tex]\$5.30\text{/lb}[/tex]. You would like to have [tex]12.5\text{ lbs}[/tex] of a nut mixture that sells for [tex]\$3.80\text{/lb}[/tex]
TO FIND: How much of each nut will you need to obtain the desired mixture.
SOLUTION:
Rate of first type of nut [tex]=\$2.80\text{/lb}[/tex]
Rate of second type of nuts [tex]=\$5.30\text{/lb}[/tex]
Total amount of nut mixture [tex]=12.5\text{ lbs}[/tex]
let the total quantity of first type of nut be [tex]=x\text{ lbs}[/tex]
quantity of second type of nuts [tex]=12.5-x \text{ lbs}[/tex]
Now,
rate of new nut mixture [tex]=\$3.80\text{/lb}[/tex]
rate of new mixture [tex]=\frac{\text{rate of first type of nuts}\times\text{quantity of first type nuts}+\text{quantity of second type of nuts}\times\text{rate of second type of nuts}}{\text{total quantity}}[/tex]putting values
[tex]\frac{2.80\times x+5.3\times(12.5-x)}{12.5}=3.8[/tex]
[tex]2.8x+5.3\times12.5-5.3x=12.5\times3.8[/tex]
[tex]2.5x=18.75[/tex]
[tex]x=7.5\text{ lbs}[/tex]
quantity of first type of nuts [tex]=7.5\text{ lbs}[/tex]
quantity of second type of nuts [tex]=12.5-7.5=5\text{ lbs}[/tex]
Hence [tex]7.5\text{ lbs}[/tex] of first type of nuts and [tex]5\text{ lbs}[/tex] of second type of nuts are required to obtain the desired mixture.
