California Assessment of Student Performance and Progress (CAASPP) Math Practice Exam

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A number is increased by 30% to give 78. What was the original number?

The correct answer is: 60

To determine the original number that, when increased by 30%, results in 78, we start by letting the original number be represented by $ x $. An increase of 30% means that the new value is 130% of the original number. This can be represented mathematically as: \[ 1.3x = 78 \] To find $ x $, we will isolate it by dividing both sides by 1.3: \[ x = \frac{78}{1.3} \] Calculating the right side: \[ x = 60 \] This calculation shows the original number was 60. When you increase 60 by 30%, you add 18 (which is 30% of 60) to get 78, confirming that the original number indeed is 60. Understanding the mechanics of percentage increases is crucial. The original number is the basis from which the percentage increase is calculated, and correctly identifying this value is key in solving similar problems.