1. 60 quarters,12 dimes
2.12 nickels, 4 dimes
3. Maybe 7.26?
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5-------6.length 39 and width 6
1. Eugenia had five times as many quarters as dimes. If the total value of her coins was $16.20, how many of each kind of coin did she have?
2. Yolanda had three times as many nickels as dimes. If the total value of her coins was $1, how many of each kind of coin did she have?
3. If 2/3 pound of coffee costs $4.84, what does one pound cost?
4. Peanuts worth $2.95/kg were mixed with cashews worth $6.25/kg to produce a mixture worth $5.00/kg. How many kilograms of each kind of nuts were used to make 33 kg of the mixture?
5. The smaller of two numbers is three more than -2 times the larger one. If four times the smaller number is subtracted from the larger number, the result is 51. Find the numbers.
6. The perimeter of a rectangle is 90 cm. The length is 15 cm more than 4 times the width. Find the dimensions of the rectangle.
7. Pure copper was mixed with a 12% alloy to produce an alloy that was 20% copper. How much of the pure copper and how much 12% alloy were used to produce 132 kg of the 20% alloy?
8. The cost of 5 boxes of small paper clups and 2 boxes of large paper clips is $49.30 seven boxes of small clips and 4 boxes of large ones cost $79.10. Find the cost of a box of each size of paper clips.
Hello!
Let the number of quarters be and the number of dimes . Since Eugenia's total is $16.20, we have . But, we also know that there are five times as many quarters as dimes, so . Now, we have two equations with two unknowns. Can you figure it out from here?
This is very similar to question 1. Try setting up the equations!
Coffee costs $4.84 for every 2/3 of a pound. Therefore, , where is the cost and is amount.
Suppose is the amount of peanuts, in kilograms, in the mixture, and is the amount of cashews. We know that the mixture is a combination of the peanuts and cashews, so . We can now set up a second equation using the costs of each substance:
.
You should be able to take it from here.
Give a name to each number, and set up the equations described in the problem. This one should be straightforward.
Again, use what you know about the relationship between a rectangle's length, width, and perimeter to set up a system of equations.
Call the mass of the pure copper , and that of the alloy . The mixture consists of the pure copper plus the alloy, so . Also, 12% of the alloy and 20% of the mixture is copper, so we have:
.
Now solve the system.
Try this on your own. Pick variables to represent the cost of each respective box size, and then use the problem description to set up a system of equations.