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Old 07-27-2007   #4
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1. Let Jay's salary be j and his wife's salary be b for better paid, therefore j = (2/3)bAfter their $2,000 raises, their combined income will be $49,000, therefore, (j + 2000) + (b + 2000) = 49000so, substitute from the first equation into the second:j = (2/3)b(j + 2000) + (b + 2000) = 49000((2/3)b + 2000) + (b + 2000) = 49000((2/3)b + 2000) + ((3/3)b + 2000) = 49000(5/3)b + 4000 = 49000(5/3)b = 45000b = 27000therefore, j = (2/3)b, so j = 18000Jay currently makes $18,000, his wife makes $27,0002. In the first rectangle, the width is W, the length is L and so W = L-6In the second rectangle, the perimeter is 54 cm and its width and length are 3 cm wider and 2 cm shorter than the first. Therefore, W2 = W + 3 and L2 = L - 2 and 2 * (W2 + L2) = 54So, the equations are:W = L - 6W2 = W + 3L2 = L - 22 * (W2 + L2) = 54So, substituting into the second equation:W2 = (L - 6) + 3W2 = L - 3and substituting into the fourth equation:2 * ((L - 3) + (L - 2)) = 542 * (2L - 5) = 544L - 10 = 544L = 64L = 16 cmSo, since W = L - 6:W = 16 - 6 = 10 cmand since W2 = W + 3:W2 = 10 + 3 = 13 cmand since L2 = L - 2:L2 = L - 2 = 16 - 2 = 14 cmSo, the dimensions of the first rectangle are width 10 cm, length 16 cm, and the dimensions of the second rectangle are width 13 cm and length 14 cm.3) Victor's money = 43 for 13 hours at 3/hour and 4/hourSo, let A be the number of after school hours and S be the number of Saturday hours, so the equations are:A + S = 133A + 4S = 43Do the same here, substitute into the second equation the information from the first equation, like so:A = 13 - SSo,3 * (13 - S) + 4S = 4339 - 3S + 4S = 43S + 39 = 43S = 43 - 39 = 4So,A = 13 - S = 13 - 4 = 9So, Victor worked 4 hours on Saturday and 9 hours after school.