The price of a pair of baseball gloves is increased by 15%. The next month, its price is further increased by 40%. This double increase in the price of the pair of baseball gloves would be equivalent to a single increase of
25%
49%
51%
55%
61%
When percentages are applied successively, they compound. After 15% increase: new price = 1.15 × original. After 40% increase on this: final price = 1.40 × 1.15 × original = 1.61 × original. This is a 61% total increase. Common mistakes include adding the percentages (15% + 40% = 55%) or using simple multiplication (15% × 40% = 6%).
To solve this problem, we need to find the equivalent single increase in price that would result in the same final price as the double increase of 15% followed by 40%.
Let's assume the original price of the baseball gloves is \$100.
After the first increase of 15%, the price becomes: \$100 + 15% of $100 = $100 + $15 = $115.
After the second increase of 40%, the price becomes: $115 + 40% of $115 = $115 + $46 = \$161.
So, the final price after the double increase is \$161.
Now, let's find the single increase that would result in the same final price of \$161.
Let the single increase be x%.
Using the formula for calculating a percentage increase, we can write:
\$100 + x% of $100 = $161.
Simplifying this equation, we have:
$100 + 0.01x * $100 = \$161.
Dividing both sides by \$100, we get:
1 + 0.01x = 1.61.
Subtracting 1 from both sides, we have:
0.01x = 0.61.
Dividing both sides by 0.01, we get:
x = 61.
Therefore, the equivalent single increase is 61%.
So, the correct answer is E) 61%.