“FUN” PROBLEMS #3
1. A reel of recording tape 500 meters long is cut into two pieces of which one is 130 meters shorter than twice the length of the other. How long is the longer piece?
Longer = 2x-130 x+2x-130 = 500 290
Shorter = x 3x = 630
Total = 500 x = 210
2. When Mr. Franz and his daughter Marie together stepped on a scale in his packing plant, the scale registered 131 kilograms. Mr. Franz weighs 6 kilograms more than 1.5 times as much as Marie. How much does he weigh?
Franz = 1.5x+6 1.5 x+x+6 = 131 81
Marie = x 2.5x = 125
Total = 131 x = 50
3. In the Apollo spacecraft, the service module weighed 3000 pounds less than 5 times the weight of the command module. The lunar module weighed 1000 pounds less than 3 times the weight of the command module. If the total weight of the three modules was 95,000 pounds, how much did each weigh?
Service = 5x-3000 5x-3000+x+3x-1000 = 95000 11,000, 32,000, 52,000
Command = x 9x-4000 = 95000
Lunar = 3x-1000 9x = 99000
Total = 95000 x = 11000
4. It is estimated that, in addition to pasturage, a dairy cow, weighing about 1000 pounds, in a year will eat just as many pounds of grain as hay, and 2 1/3 times as many pounds of silage as hay. If the cow eats 11,700 pounds of grain, hay, and silage, how many pounds of each does she eat?
Grain = x x+x+7/3 x = 11,700 2,700, 2,700, 6,300
Hay = x 13/3 x = 11,700
Silage = 7/3 x x = 2,700
Total = 11,700
5. Behind her house Mrs. Vickers has a rectangular garden whose length is 20 feet less than twice its width. On three sides of the garden she installed a chain link fence, but left open the long side facing her housing. She used 100 feet of fencing. Find the dimensions of her garden.
Length = 2x-20 x+x+2x-20 = 100
Width = x 4x - 20 = 100
Total (three sides) = 100 4x = 120
x = 30 30 x 40
6. Mr. Polsky, a packaging expert, designed a rectangular box having two square faces. The other four faces of the box were rectangles, each 1 inch longer than twice as long as it was wide. The sum of the length (along the longest edge) and the girth of the box was 85 inches. What were the dimensions (length, width, and height) of the box?
Length = 2x+1 (2x+1)+x+x+x+x = 85
Width = x 6x+1 = 85
Height = x 6x = 84 14, 14, 29
Girth = 4x x = 14
7. Mr. Dollard has 3 times as many eight-cent stamps as ten-cent stamps and 6 more four-cent stamps than ten-cent stamps. In all, he has 16 stamps. Does he have enough stamps to mail a parcel for which the postage is 80 cents? Explain. YES 32 cents +20 cents +48 cents = $1.00
8 cents = 3x 3x+x+x+6 = 16 2, 6, 8
10 cents = x 5x = 10
4 cents = x+6 x = 2
8. The three members of the Art Department have taught a combined total of 39 years. Mr. Sargent has taught 8 years longer than Miss Gonzales. How Long has each instructor taught?
Not Enough Information
9. One side of a triangular lot is 10 feet shorter than three times as long as the second side. The third side is 9 feet shorter than the first side. The perimeter of the lot is 90 feet. How long is each side?
1st side = 3x-10 3x-10+x+3x-19 = 90 17, 32, 41
2nd side = x 7x-29 = 90
3rd side = 3x-19 7x = 119
Perimeter = 90 x = 17