Our problem solving strategies will still apply here, but we will add to the first step. We will use the distance, rate, and time formula, D = r t, D = r t, to compare two scenarios, such as two vehicles travelling at different rates or in opposite directions. We call a problem in which the speed of an object is constant a uniform motion application. When you are driving down the interstate using your cruise control, the speed of your car stays the same-it is uniform. If she wants to make 28 gallons of punch at a cost of $3.25 a gallon, how many gallons of fruit juice and how many gallons of soda should she buy? Solve Uniform Motion Applications She can buy fruit juice for $3 a gallon and soda for $4 a gallon. Henning mixed ten pounds of raisins with 15 pounds of nuts.īecca wants to mix fruit juice and soda to make a punch. The information for the total amount of the Notice that the last column in the table gives We multiply the number times the value to get the total value.Ģ5 − x = 25 − x = number of pounds of nuts We enter the price per pound for each item. Represent the number of each type of ticket using variables.Īs before, we fill in a chart to organize our information. The 25 pounds of trail mix will come from mixing raisins and nuts. They sold 26 full-fare and 14 reduced-fare tickets. There were 26 full-fare tickets at $32 each and 14 reduced-fare tickets at $26 each. Write the equation by adding the total values of each type of ticket. Multiply the number times the value to get the total value of each type of ticket. This means the number of reduced-fare tickets is 40 less the number of full-fare tickets. We know the total number of tickets sold was 40. Represent the number of each type of ticket using variables.Ĥ0 − f = 40 − f = the number of reduced-fare tickets The number of full-fare tickets and reduced-fare tickets Determine the types of tickets involved.įull-fare tickets and reduced-fare tickets We will apply this technique in the next example. In each case, we subtracted the number of child tickets from 100 to get the number of adult tickets. Then how many adult tickets did he sell? To find out, we would follow the same logic we used above. Now, suppose Aniket sold x child tickets. If he sold 45 child tickets, how many adult tickets did he sell?ĭid you say “55”? How did you find it? By subtracting 45 from 100? If he sold 20 child tickets, how many adult tickets did he sell?ĭid you say “80”? How did you figure that out? Did you subtract 20 from 100? Each ticket was either an adult ticket or a child ticket. Suppose Aniket sold a total of 100 tickets. In our next example, we have to relate the quantities in a different way. In most of our examples so far, we have been told that one quantity is four more than twice the other, or something similar. How many 49-cent stamps and how many 20-cent stamps did Kailee buy? The number of 49-cent stamps was four less than three times the number of 20-cent stamps. Write the equation by adding the total value of all the types of coins. Get the total value of each type of coin. In the chart, multiply the number and the value to The number of nickels is three more than eight times Number of pennies, so start with pennies. The number of nickels is defined in terms of the Represent the number of each type of coin using variables.
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