Rachel can buy licorice sticks for $0.75 and cherry candies for $0.50 and has a budget of $25. If her expenses are represented by the equation 0.75x + 0.5y = 25, where x is the number of licorice sticks and y is the number of cherry candies, how many cherry candies can she buy if she wishes to spend the entire $25 on cherry candies? (Note: x ≥ 0, y ≥ 0, and x and y take only integer values.

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sammixboo · Answer

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ciarán95 · Answer

If she wishes to spend an entire $25 on cherry candies, then she is clearly not spending any money on licorice sticks. So, we can simplify the equation, as x will always be zero, to
$$0.5y = 25$$
So here we are looking for y, the number of cherry candies she can buy for $25, with each costing $0.50 each. You can probably work this out in your head, but if you want we can use the new equation to get y on its own to find the answer. If we divide both sides of the equation by 0.5, we get:
$$\frac{ 0.5y }{ 0.5 } = \frac{ 25 }{ 0.5 }$$
The two 0.5s on the left-hand side cancel and we are left with:
$$y = \frac{ $25 }{ $0.50 }$$
If you work this out, this should give you the number of cherry candies Rachel can buy. Hope that helped! :)