   Chapter 4.1, Problem 66E Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Diet The local sushi bar serves 1-ounce pieces of raw salmon (consisting of 50% protein) and 1 1 4 -ounce pieces of raw tuna (40% protein). A customer's total intake of protein amounts to 1 1 2 ounces after consuming a total of three pieces. How many of each type did the customer consume? (Fractions of pieces are permitted.)

To determine

To calculate: The number of pieces of each type of fish, raw salmon and raw tuna customer consumed, if the local sushi bar serves to the customer, 1-ounce piece of raw salmon (consisting of 50% protein) and 114-ounce pieces of raw tuna (40% protein).

Explanation

Given Information:

The local sushi bar serves to the customer, 1-ounce piece of raw salmon (consisting of 50% protein) and 114-ounce pieces of raw tuna (40% protein). A customer consume total of three pieces total and then intake of protein amounts to 112 ounces.

Formula used:

Elimination method:

Step 1: Consider the linear equations in two variables.

Step 2: The equations are multiplied with suitable non-zero numbers to convert the coefficients to equals of opposite signs.

Step 3: The equations are combined to eliminate one variable, and the value of the other variable is calculated.

Step 4: Substitute the value of the calculated variable into one of the equations and calculate the value of the other variable.

For any real z, z%=z100.

Calculation:

Consider the problem,

Let x be the number of pieces of raw salmon and y be the number of pieces of Raw tuna.

Here, if the customer consumes x pieces of raw salmon and y pieces of raw tuna, then total number of pieces consumed by the customer is x+y. But a customer consume total of three pieces total and then intake of protein amounts to 112 ounces.

Thus,

x+y=3

Also, the local sushi bar serves to the customer, 1-ounce piece of raw salmon (consisting of 50% protein) and 114-ounce pieces of raw tuna (40% protein).

Substitute z=50 in z%=z100,

50%=50100=0.5

Raw salmon contains 50% of 1-ounce protein.

Thus, 50% of 1-ounce=0.5(1)=0.5 ounce per piece.

Also, substitute z=40 in z%=z100

40%=40100=0.4

Raw tuna contains 40% of 114 ounce protein.

Thus, 40% of 114 ounce is 0.4(114)=0.4(54)=0.5 ounce per piece.

Also, a customer’s total intake of protein amounts to 112=32=1.5 ounces.

Thus,

0.5x+0.5y=1.5

Consider the equation 0.5x+0.5y=1.5,

Multiply both sides of equation 0

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