Question 1202330
<pre>
Sarah had some money in the piggy bank. On Monday, she took out 2/5 of the money to buy a present. She had $78 left and she put it back into the piggy bank. On Tuesday, she took out 3/8 of the money to buy some story books. She had $28.80 left and she put it back into the piggy bank. After that, she found that there was $246.30 in the piggy bank. How much money did she have in the piggy bank at first?

Let initial amount in piggy bank be A
After taking out {{{matrix(1,3, (2/5)A, or, 2A/5)}}}, she had {{{matrix(1,3, (1 - 2A/5), or, 3A/5)}}} remaining
Since the remainder from the {{{2A/5}}}, was $78, then after placing the $78 back, there was {{{3A/5 + 78}}} in the piggy bank

On Tuesday, {{{3/8}}} of remainder was taken out leaving {{{5/8}}} of remainder or {{{matrix(1,5, 5/8, of, (3A/5 + 78), or, 3A/8 + 195/4)}}}

     After placing the $28.80 back into the piggy bank, she then had {{{3A/8 + 195/4 + 28.8}}}

  Since the final amount in the piggy bank was $246.30, we then get: {{{matrix(3,3, 3A/8 + 195/4 + 28.8, "=", 246.3, 3A/8, "=", 246.3  -  28.8  -  195/4, 3A/8, "=", 217.5  -  195/4)}}} 
                                                                                 3A = 1,740 - 390 -------- Multiplying by LCD, 8
                                                                                 3A = 1,350
                                                Initial amount in piggy bank, or {{{highlight_green(matrix(1,5, A, "=", "1,350"/3, "=", highlight("$450")))}}}</pre>