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A local grocer wants to mix candied pecans, priced at \$14.00/$14.00/dollar sign, 14, point, 00, slashpound (\text{lb})(lb)(, start text, l, b, end text, ), and candied cashews, priced at \$10.00/\text{lb}$10.00/lbdollar sign, 10, point, 00, slash, start text, l, b, end text. How many pounds of candied cashews must he mix with 8\,\text{lbs}8lbs8, start text, l, b, s, end text of candied pecans to make a mixture that costs \$12.50/\text{lb}$12.50/lbdollar sign, 12, point, 50, slash, start text, l, b, end text? (Round the answer to the nearest tenth of a pound.)

Respuesta :

pedrocarratore

Answer:

4.8 lbs

Step-by-step explanation:

Candied pecan price: $14.00

Candied Cashew price: $10.00

Mixture price: $12.50

Candied cashew weight: x lbs

Candied pecan weight: 8 lbs

Mixture weight: y pounds

The sum of the weights of candied pecan and candied cashew must equal the weight of the mixture. While the mixture weight multiplied by the mixture price must equal the sum of each individual candy's weight multiplied by its price:

[tex]x+8 = y\\14*8 + x*10 = y*12.50[/tex]

Multiplying the firs equation by -10 and adding it to the second one, gives us the value of "y" which can then be used to find "x":

[tex]112 + 10x - 10x-80 = 12.50y - 10y\\2.5y = 32\\y=\frac{32}{2.5}=12.8\\x = 12.8 - 8\\x = 4.8[/tex]

Therefore, the grocer would need 4.8 pounds of candy cashews to make the mixture.

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