Math Problem Statement
Miko likes arranging fruit platters. In a fruit platter competition Miko joined, the ratio of apples to papayas the organiser prepared was 1: 5. If 92 papayas were added, the ratio of apples to papayas would be 1: 7. How many apples were there?
Solution
Let the number of apples be , and the number of papayas be .
We are given the following two pieces of information:
- Initially, the ratio of apples to papayas is 1:5, which means:
- After 92 papayas are added, the new ratio of apples to papayas becomes 1:7, so:
Step 1: Express in terms of
From the first equation, we know that .
From the second equation, we have .
Since both expressions represent , we can set them equal to each other:
Step 2: Solve for
Multiply both sides by 35 to eliminate the denominators:
Expand the right side:
Subtract from both sides:
Solve for :
Step 3: Find
Now that we know , substitute this value into the first equation to find :
Thus, the number of apples is .
Would you like further clarification or details on the solution?
Here are 5 related questions to explore:
- If 10 more papayas were added to the final scenario, what would the new ratio be?
- How many papayas were there initially in the competition?
- What if the initial ratio was 1:4 instead of 1:5, and the same number of papayas were added?
- What is the percentage increase in the number of papayas after 92 were added?
- How would the ratios change if 20 apples were added instead?
Tip: When solving ratio problems, it's helpful to express unknowns in terms of one variable and use systems of equations to simplify the solution.
Ask a new question for Free
By Image
Drop file here or Click Here to upload
Math Problem Analysis
Mathematical Concepts
Ratios
Algebra
Systems of Equations
Formulas
Ratio formula: a/p = 1/5
a = 1/5 * p
a = 1/7 * (p + 92)
Solving linear equations
Theorems
Basic ratio properties
Equation solving methods
Suitable Grade Level
Grades 6-8