How do I solve this type of problem? How many steps are there.
The cost of a membership at a health club last year was 75% of the cost at the club this year. This year's membership costs $20 more than last year's membership. Find the cost of a membership last year and the cost of a membership this year.
Simplifying
x = 0.75(x + 20)
Reorder the terms:
x = 0.75(20 + x)
x = (20 * 0.75 + x * 0.75)
x = (15 + 0.75x)
Solving
x = 15 + 0.75x
Solving for variable 'x'.
Move all terms containing x to the left, all other terms to the right.
Add '-0.75x' to each side of the equation.
x + -0.75x = 15 + 0.75x + -0.75x
Combine like terms: x + -0.75x = 0.25x
0.25x = 15 + 0.75x + -0.75x
Combine like terms: 0.75x + -0.75x = 0.00
0.25x = 15 + 0.00
0.25x = 15
Divide each side by '0.25'.
x = 60
Simplifying
x = 60
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last year = x
this year = x+20
x = 0.75(x+20)
Thanks. Membership last year was $60 and membership this year is $80.
To solve this problem, we can follow a few steps:
Step 1: Let's assume the cost of the membership last year was x dollars.
Step 2: According to the problem, the cost of the membership this year is $20 more than last year's membership, so the cost this year is (x + $20).
Step 3: We are given that the cost of a membership at the health club last year was 75% of the cost this year. This can be written as 0.75(x + $20) = x.
Step 4: Now, we can solve this equation to find the value of x, which represents the cost of the membership last year.
To solve the equation:
Step 5: Distribute 0.75 to the terms inside the parentheses: 0.75x + 0.75($20) = x.
Step 6: Simplify the equation by multiplying out the terms: 0.75x + $15 = x.
Step 7: Move 0.75x to the right side of the equation by subtracting it from both sides: $15 = x - 0.75x.
Step 8: Combine like terms on the right side: $15 = 0.25x.
Step 9: Divide both sides by 0.25 to isolate x: $15 / 0.25 = x.
Step 10: Calculate the value of x: $60 = x.
Therefore, the cost of a membership last year was $60, and the cost of a membership this year is $60 + $20 = $80.