Answer: Their total budget last year was $40,000. Step-by-step explanation: Given : The Smiths spend 6% of their budget on entertainment. i.e. , The money they spend on entertainment = 0.06 x ( Total budget) { 6% is converted to 0.06 , when we divide it by 100 to remove percentage) Since , this year they plan to spend $2,580 on entertainment. i.e. 0.06 x ( Total budget ) = $2,580 On dividing both sides by 0.06 , we get ( Total budget ) = $2,580 ÷ 0.06 = $43,000 Thus , their total budget for this year = $43,000 Also, Their total budget this year is $3,000 more than last year. Therefore , their last year total budget = ( Total budget this year ) - $3000 = $43,000 - $3000 = $40,000 Hence, their total budget last year was $40,000.
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If the absolute value expression is not equal to zero, the expression inside an absolute value can be either positive or negative. So, there can be at most two solutions. Looking at this graphically, an absolute value graph can intersect a horizontal line at most two times.