Algebra 1 Glencoe McGraw-Hill JoAnn Evans Mixed Problem Solving Practice

Two cars, 700 miles apart, decide to travel until they meet. One leaves 4 hours ahead and travels at 30 mph. The other leaves going 50 mph. How long after the second car leaves will the two cars meet? Let x = 2 nd car’s time Let x + 4 = 1 st car’s time distance of 1 st car + distance of 2 nd car = total distance 30(x + 4) + 50x = x x = x = 580 x = 7.25 They’ll meet 7.25 hours after the second car leaves. 700 miles 1 st 2 nd

Alicia has 8 more nickels than quarters. The total value of her coins is $3.70. How many of each coin does she have? Let x = # quarters Let x + 8 = # nickels value of quarters + value of nickels = total 25x + 5(x + 8) = x + 5x + 40 = x = 330 x = 11 Alicia has 11 quarters and 19 nickels. Let 25x = value of quarters Let 5(x + 8) = value of nickels

Bob can paint a small house in 20 hours. Ray could paint the same house in 16 hours. How long would the job take if Bob and Ray worked together? Let x = time to do the job together Bob’s work done + Ray’s work done = 1 house painted

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Hector built a rectangular fish pond that is surrounded by a brick sidewalk that’s 2 meters wide. The area of the sidewalk is 76 m 2. Find the dimensions of the pond if it is twice as long as it is wide. Let x = pond width Let 2x = pond length 2x x 2 + 2x x + 2 Let x + 4 = total width Let 2x + 4 = total length area of pond + area of brick walk = total area 2x(x) + 76 = (2x + 4)(x + 4) 2x = 2x 2 + 8x + 4x = 12x = 12x 5 = x The pond is 5 meters by 10 meters.

The length of a rectangle is 4 more than its width. The perimeter of the rectangle is 34 more than twice the length. Find the dimensions of the rectangle. Let w = width Let w + 4 = length Perimeter = two times the length w + 2(w + 4) = 2(w + 4) w + 2w + 8 = 2w w + 8 = 2w w = 34 The rectangle is 17 units by 21 units. w + 4 w w = 17

The snack mix will contain 9 lbs. of M&Ms and 6 lbs. of peanuts. · · · 200x (15 – x) = x – 150x = x = x = 450 x = 9 cost amount + cost amount = cost amount M&Ms peanuts snack mix M&Ms selling for $2/lb are mixed with peanuts selling for $1.50/lb to make 15 lbs. snack mix that will sell for $1.80/lb. How many pounds of M&Ms and how many pounds of peanuts are contained in the mix? Let x = # lbs. of M&MsLet 15 - x = # lbs. of peanuts