Answer:
Liliana has $2.10 in nickels and quarters in her backpack. She has 12 more nickels than quarters. How many coins of each type does she have?
Step-by-step explanation:
Multiply: 14(0.25). If you missed this problem, review Example 5.3.5.
Simplify: 100(0.2 + 0.05n). If you missed this problem, review Example 7.4.6.
Solve: 0.25x + 0.10(x + 4) = 2.5 If you missed this problem, review Example 8.6.8.
Imagine taking a handful of coins from your pocket or purse and placing them on your desk. How would you determine the value of that pile of coins?
If you can form a step-by-step plan for finding the total value of the coins, it will help you as you begin solving coin word problems.
One way to bring some order to the mess of coins would be to separate the coins into stacks according to their value. Quarters would go with quarters, dimes with dimes, nickels with nickels, and so on. To get the total value of all the coins, you would add the total value of each pile.Figure 9.3.1 - To determine the total value of a stack of nickels, multiply the number of nickels times the value of one nickel.For coins of the same type, the total value can be found as follows:
number⋅value=totalvalue(9.3.1)
where number is the number of coins, value is the value of each coin, and total value is the total value of all the coins.
You could continue this process for each type of coin, and then you would know the total value of each type of coin. To get the total value of all the coins, add the total value of each type of coin.
Let's look at a specific case. Suppose there are 14 quarters, 17 dimes, 21 nickels, and 39 pennies. We'll make a table to organize the information – the type of coin, the number of each, and the value.
Table 9.3.1
Type Number Value ($) Total Value ($)
Quarters 14 0.25 3.50
Dimes 17 0.10 1.70
Nickels 21 0.05 1.05
Pennies 39 0.01 0.39
6.64
How would you determine the value of each pile? Think about the dime pile—how much is it worth? If you count the number of dimes, you'll know how many you have—the number of dimes.
But this does not tell you the value of all the dimes. Say you counted 17 dimes, how much are they worth? Each dime is worth $0.10 —that is the value of one dime. To find the total value of the pile of 17 dimes, multiply 17 by $0.10 to get $1.70. This is the total value of all 17 dimes.
