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Algebra

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A store is having a sale on almonds and jelly beans. For 3 pounds of almonds and 5 pounds of jelly beans, the total cost is $24. For 9 pounds of almonds and 7 pounds of jelly beans, the total cost is$42. Find the cost for each pound of almonds and each pound of jelly beans.

Feb 9, 2022

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Let x be the cost for one pound of almond and y be the cost for one pound of jelly bean

Making a system of equations:

$$3x + 5y = 24$$

$$9x+7y = 42$$

Multiplying the first equation by -3 and we get

$$-9x- 15y = -72$$

$$9x +7y = 42$$

Then we add both equations together

$$y = \frac{30}{8} = \boxed{3.75}$$

Then we plug 3.75 in for y in the first equation

$$3x + 5(3.75) = 24$$

$$3x + 18.75 = 24$$

$$3x = 5.25$$

$$x = \boxed{1.75}$$

So one pound of almond cost $$1.75$$ and one pound of jelly bean cost $$3.75$$.

Feb 9, 2022