Mia is mixing nuts and cereal squares to make 12 pounds of trail mix. Nuts costs $8 a pound and cereal squares cost $3 a pound. If Mia wants her cost For the trail mix to be $5.50 a pound how many pounds of nuts and how many pounds of cereal squares should she use?

Question

Mathematics

Terrance Heath

18 June, 00:41

Mia is mixing nuts and cereal squares to make 12 pounds of trail mix. Nuts costs $8 a pound and cereal squares cost $3 a pound. If Mia wants her cost For the trail mix to be $5.50 a pound how many pounds of nuts and how many pounds of cereal squares should she use?

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Answers (1)

Know the Answer?

Bernard Lara · Answer 1

Weight of nuts = 6 pounds.

Weight of cereal squares = 6 pounds.

Step-by-step explanation:

Let the weight of nuts used in the trial mix to be x pounds and the weight of cereal squares used in the trial mix to be y pounds. Total weight of the mixture is 12 pounds. Therefore: x + y = 12. This implies y = 12 - x (Equation 1).

Cost of nuts per pound = $8 and cost of cereal squares per pound = $3. Cost of the mixture per pound = $5.5. Total mixture = 12 pounds. Since x pounds of nuts and y pounds of cereal squares are used, therefore: 8x + 3y = 5.5 * 12.

8x + 3y = 66. (Equation 2).

Put equation 1 in equation 2.

8x + 3 (12 - x) = 66.

8x + 36 - 3x = 66.

5x = 30.

x = 6.

Put x = 6 in equation 1.

y = 12 - 6.

y = 6.

Therefore, the weight of nuts used in the trial mix will be 6 pounds and the weight of cereal squares used in the trial mix will be 6 pounds!