4). Problem type: Solving 2 simultaneous equations
Example:
Parmveer has a bag with 54 coins. Altogether the coins are worth $4.75. He only has nickels and dimes in the bag. How many dimes are in the bag?
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Solution:
Use N for the number of nickels and
D for the number of dimes.
1. The equation for the number of coins:
N + D = 54
2. The equation for the sum of the coins:
5N + 10D = 475
3. Write an expression for N using the first equation and then substitute it in the second equation and solve.
N = _____
D = _____
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5). Problem type: Permutations
Example:
Roxanne is ordering a pizza. She can choose from 3 sizes, 3 types of crust, 4 blends of sauce, and
6 toppings. How many pizza combinations are possible if she orders a pizza with 2 toppings?
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Solution:
First, remember that these are combinations where
the order of selecting toppings doesn't count.
1. How many ways can she choose a size = ___
2. How many ways can she choose a crust = ___
3. How many ways can she choose a sauce = ___
4. How many ways can she choose that first topping? ____
5. After she chooses that first topping, how many ways can she choose the second topping? = ___
6. Total choices of toppings = ____
7. Since order of toppings doesn't count, take half of the topping choices = _____
8. Multiply these together = _____
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6.) Problem type: Working a problem backwards
Example:
Quint bought a car. He sold it to Rachael for 5/6 of the price he paid for it. Rachael sold
it to Shawn for 1/5 less than she paid for it. Shawn sold it to Teddy for 3/4 of what he paid.
Teddy paid $1200 for it. How much did Quint pay for it originally?
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Solution:
Use Q for Quint, R for Rachael, S for Shawn and T for Teddy.
Start at the bottom:
1. If Teddy paid $1200 for the car and it was 3/4
of what Shawn paid, then 1200 = (3/4) x S.
So S = ______
2. Rachael sold it to Shawn for 4/5 of what she paid Quint for it, so
(4/5) R = S, and R = ____.
3. Continue this logic until you solve for Q:
Q = _____
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Example:
