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Calvin mixes candy that sells for .00 per pound with candy that costs .60 per pound to make 50 pounds of candy selling for .16 per pound.How many pounds of each kind of candy did he use in the mix?
At the end of one interest period, the total interest earned was $278. The last column gives an equation which can be solved for x: Then , so $2100 was invested at and $5900 was invested at . The first few involve mixtures of different things which cost different amounts per pound.
For instance, if you have 4 pounds of candy which costs $2 per pound, the total cost of the candy is In other words, the number of pounds times the price per pound is the total cost.
The first and third columns give two equations: Multiply the first equation by 2 and subtract equations: Then He used 45 pounds of the $2 candy and 5 pounds of the $3.60 candy.
Phoebe wants to mix raisins worth $1.60 per pounds with nuts worth $2.45 per pound to make 17 pounds of a mixture worth $2 per pound.
A total of 78 seats for a concert are sold, producing a total revenue of $483.
If seats cost either .50 or .50, how many .50 seats and how many .50 seats were sold?In other cases, you set two of the numbers in a column equal, or subtract one number from another.There is no general rule for telling which of these things to do: You have to think about what the problem is telling you. (ii) Adding equation (i) and (ii), we get 2x = 16 or, 2x/2 = 16/2 or, x = 16/2 or, x = 8 Substituting the value x in equation (i), we get 8 y = 14 or, 8 – 8 y = 14 - 8 or, y = 14 - 8 or, y = 6 Therefore, x = 8 and y = 6 Hence, the two numbers are 6 and 8. If 36 is added to the number, digits interchange their places, Therefore, we have 10y x 36 = 10x y or, 10y – y x 36 = 10x y - y or, 9y x – 10x 36 = 10x - 10x or, 9y - 9x 36 = 0 or, 9x - 9y = 36 or, 9(x - y) = 36 or, 9(x - y)/9 = 36/9 or, x - y = 4 ………. Then x = 3y and the number = 10y x The number obtained by reversing the digits is 10x y.The first and third columns give the equations Multiply the second equation by 100 to clear the decimals. Suppose you have 50 pounds of an alloy which is silver.This gives Solve the equations by multiplying the first equation by 160 and subtracting it from the second: Hence, and . Then the number of pounds of (pure) silver in the 50 pounds is That is, the 50 pounds of alloy consists of 10 pounds of pure silver and pounds of other metals. Suppose you have 80 gallons of a solution which is acid.But they are convenient for organizing information --- and they give you a pattern to get started with problems of a given kind (e.g.interest problems, or time-speed-distance problems). In some cases, you the numbers in some of the columns in a table.If I have 6 tickets which cost each, the total cost is If I have 8 dimes, the total value is This is common sense, and is probably familiar to you from your experience with coins and buying things.But notice that these examples tell me what the general equation should be: The number of items times the cost (or value) per item gives the total cost (or value). The total value of the coins (880) is the value of the pennies will go in the third column.