more math questions.. really sorry..? - XP Math - Forums

 XP Math - Forums more math questions.. really sorry..?

 07-27-2007 #1 Chocolate Guest   Posts: n/a more math questions.. really sorry..? 1) Jay's salary is 2/3 of his wife's salary. In Jan., wen they both get \$2000 raises, their combined income will be \$49000. What are their current incomes? 2) A width of a rectangle is 6 cm less than the length. A second rectangle, with a perimeter of 54 cm, is 3 cm wider and 2 cm shorter than the first. What are the dimensions of each rectangle? 3) Victor earns \$3 an hr working after school and \$4 an hour wokring on Saturdays. Last week he earned \$43, working a total of 13 hrs. How many hours did he work on Saturday? could u show me how you did the question? thanks so much.
 07-27-2007 #2 Mr. Scientist Guest   Posts: n/a It seems like you are asking alot of word problem questions. Try to assign variables to each item in the question that you need to figure out. Then make an equation with those variables and the numbers from the problem.I'll help with the first one."Jay's salary is 2/3 of his wife's salary."so...Wife's salary = x (just choose a variable)Jay's salary = 2/3 * x or just 2/3 x (2/3 of his wife's)"In Jan., wen they both get \$2000 raises, their combined income will be \$49000."Jay's (2/3x) + \$2000 + wife's (x) + \$2000 = \$490002/3x + 2000 + x + 2000 = 49000x + 2/3x + 4000 = 490005/3x = 450005x = 135000 (multiply both sides by 3)x = 27000 (divide both sides by 5)What are their current incomes?*tricky question, they have NOT gotten their Jan. raises yet.*Wife's salary = x = \$27000Jay's salary = 2/3x = \$18000 (27000 x 2/3)So just read your questions, and try to make an equation out of them.Good luck!
 07-27-2007 #3 JAMES M Guest   Posts: n/a 1)\$49000-\$4000=\$45000 \$45000/5=\$9000 \$9000*2=\$18000 \$18000+\$2000=\$20000 \$49000-\$20000=\$29000 Jay has \$20000 and wife has \$290002)large rectangle has a width of 14cm and height of 13cm width14cm +3=17 height13-2=11 17-11=6 so small rectangle width 17cm and height of 11 cm3)x+y=13hrs 3x+4y=43 (4*4)+(9*3)=\$43 so he worked 4 hours on saturday
 07-27-2007 #4 N E Guest   Posts: n/a 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.

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