High School

Ryan and Maria each improved their yards by planting hostas and geraniums. They bought their supplies from the same store.

Ryan spent $96 on 6 hostas and 8 geraniums. Maria spent $64 on 5 hostas and 4 geraniums.

What is the cost of one hosta and the cost of one geranium?

Answer :

Final answer:

By setting up equations using the information given for Ryan and Maria's purchases and applying the elimination method, we find that one hosta costs $8 and one geranium costs $6.

Explanation:

Ryan and Maria are trying to figure out the cost of individual hostas and geraniums based on their total spending at the store. We have two equations from the information they provided:

  • Ryan: 6H + 8G = $96
  • Maria: 5H + 4G = $64

To solve these equations, we can use the method of substitution or elimination. Let's use the elimination method:

  1. Multiply Maria's entire equation by 2 to align the number of geraniums with Ryan's equation.
  2. 10H + 8G = $128 (Maria's doubled equation)
  3. Subtract Ryan's equation from Maria's doubled equation.
  4. (10H + 8G) - (6H + 8G) = $128 - $96
  5. 4H = $32
  6. Divide both sides by 4 to find the cost of one hosta: H = $8
  7. Substitute the cost of one hosta back into any of the original equations to find the cost of one geranium.
  8. 5H + 4G = $64 becomes 5($8) + 4G = $64
  9. 40 + 4G = $64
  10. Subtract 40 from both sides: 4G = $24
  11. Divide both sides by 4 to find the cost of one geranium: G = $6

Therefore, one hosta costs $8 and one geranium costs $6.

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