Rosa bought a bag of apples. After she baked pies, she had 2/3 of a bag left. Then she gave her cousin 3/4 of these, which was 9 apples How many apples did Rosa have to start?

Great algebra problem! We need to represent the unknown (which is the number of apples Rosa started with) with a letter, such as x.

After baking the pies, Rosa had (2x/3) apples left.

She gave her cousin (3/4) of (2x/3) apples. This comes out to x/2 apples, which is 9 apples, according to the problem.

Solve x/2 = 9 for x.

Be certain to check your answer!

After baking the pies, she had 2/3 of a bag left, which is (2/3) of 18, or 12.

Is (3/4) of 12 equal to 9?

Draw your own conclusions. Is x = 18 or not? Justify your answer.

Rosa had 18 apples to start with. If she gave her cousin 9 apples which was 3/4 of what she had left, 9/3=3 and 3x4=12. If she had 12 apples left when she had 2/3 of a bag left, 12/2=6 and 6x3=18. She had 18 apples in the beginning.