Q36. - Algebra 2

Question

For Exercises 36 and 37, use the following information.

The Harvest Nut Company sells made-to-order tail mixes. Santito’s favourite mix contains peanuts, raisin, and carob-coated pretzels. Peanuts sell for $3.20$ per pound, raisins are $2.40$ per pound, and the carob-coated pretzels are $4.00$ per pound. Santito chooses to have twice as many pounds of pretzels as raisins, wants 5 pounds of mix, and can afford $16.80$.

Write a system of three equations using the information given.

Step-by-Step Solution

Answer

The required system of equations is,

$x+y+z=5$

$z=2y$

$3.2x+2.4y+4z=16.80$

Step 1- Determine the base on which the equations can be formed

Consider that the variable x represents the amount of peanuts, y represents the amount of raisin and z represents the amount of carob-coated pretzels. Each amount is in pound.

The first equation can be formed on the basis of amount of each nut in which the amount of each nut added together that will be equal to 5. The second can be formed on the basis provided quantity related to pretzels and raisins. The third can be formed on the basis of price of each fruit added together that will be equal to $16.80$.

Step 2 – Form the system of equations by using the bases

Use the provided table and obtained bases then form both of the equations.

$x+y+z=5$

$z=2y$

$3.2x+2.4y+4z=16.80$

Step 3- Make the conclusion

As the obtained system of equations is representing the values which are in provided information which means that the obtained equations are the required equations.