Case (1): It is impossible to have 19 coins of the same type that equal one dollar.
19 pennies = 19 cents 19 nickels = 95 cents 19 dimes = $1.90 (too big so quarters and half dollars are also eliminated)
Case (2): There are TWO ways to have one dollar using only two types of coins.
10 pennies and 9 dimes = $1 18 nickels and 1 dime = $1
Case (3): There are THREE ways to have one dollar using only three types of coins.
15 pennies, 1 dime, and 3 quarters = $1 10 pennies, 8 nickels, and 1 half dollar = $1 5 pennies, 9 nickels, and 5 dimes = $1
Case (4): There are FOUR ways to have one dollar using only four types of coins.
15 pennies, 2 nickels, 1 quarter, and 1 half dollar = $1 10 pennies, 3 nickels, 5 dimes, and 1 quarter = $1 10 pennies, 6 nickels, 1 dime, and 2 quarters = $1 5 pennies, 12 nickels, 1 dime, and 1 quarter = $1
Case (5): It is impossible to have all five types of coins.
Suppose we did have all five types of coins. We could have at most one half dollar. So we have accounted for 50 cents. That leaves 50 cents for the other four types of coins. If we are to have all four types then we can have at most one quarter (25 cents). We must now split the remaining 25 cents among the dimes, nickels, and pennies. If we have just one dime, one nickel, and one penny (16 cents), then the remaining 9 cents must be in pennies (i.e. 9 pennies) or made up of another nickel and 4 more pennies. We now have
10 pennies, 1 nickel, 1 dime, 1 quarter, and 1 half dollar = $1 or 5 pennies, 2 nickels, 1 dime, 1 quarter, and 1 half dollar = $1
However, we only have 10 + 1 + 1 + 1 + 1 = 14 coins or 5 + 2 + 1 + 1 + 1 = 10 coins ( not the 19 coins we wanted).
Therefore, it is impossible to use all five types of coins to get 19 coins to equal one dollar.
How many dimes do you need to make 70 cents? seven (7) How many nickels do you need to make 25 cents? five (5) How many pennies does it take to make 1 dollar? one-hundred (100) How many nickels does it take to make 50 cents? ten (10)
Answer: 100 pennies, 20 nickels, 10 dimes, or 4 quarters; each = 1 dollar. Can you make a dollar using only 7 coins? Answer: 2 quarters + 5 dimes = 1 dollar.
The possible values are less than 4 but greater than -4.
In the given statement is :
Javier writes an integer on a piece of paper. The absolute value of his number is less than 4.
What is Inequality?
Inequality, a statement of an order relationship - greater than, greater than or equal to, less than, or less than or equal to -- between two numbers or algebraic expressions.
Let the integer written by Javier be x
Thus, According to the given situation
=> x > 4 and -x > 4
=> x > 4 and x < -4 (by multiplied -1 on both sides , the inequality reverse)
=> -4 < x< 4
The possible values are less than 4 but greater than -4
a. The bridge can hold at most 1000 pounds. This tells you everyone's accumulative weight needs to be less than or equal to 1000. The problem does not give your friend's weight... yet. Let x = your friend's weight.
Your friend's weight (x) plus your weight (156) plus everyone else's weight (675) must be less than or equal to (≤) 1000 pounds.
x + 156 + 675 ≤ 1000
Combine like terms (the constants) to simplify and get your final inequality:
x + 831 ≤ 1000
b. Now, we find out your friend weighs 182 pounds. x = 182. We plug this into the above equation. If it results in a true statement, then you both can walk across the bridge.
182 + 831 ≤ 1000
1013 ≤ 1000, is not a true statement.
No. You both cannot walk across the bridge as is because the weight of the people on the bridge would be 13 pounds over the weight limit.
