Zachary saved x nickels and y dimes last month. Lily saved x nickels and 2y dimes. Lily saved $2 more than Zachary and the total number of her dimes is 4 times the total number of her nickels.
a) How many coins does Zach have?
b) How much did Lily save?
c) How much did Zachary save?
Needs to be modeled using Singapore Math!
Eq1,Lily: 5*x + 10*2y = 5*x + 10*y + 200.
Replace 2y with 4x and y with 2x:
Lily: %*x + 10*4x + %5*x + 10*2x + 200.
5x + 40x = 5x + 20x + 200
X = 10 nickels.
In Eq1, replace X with 10 and solve for Y:
50 + 20y = 50 + 10y + 200
Y = 20 dimes.
a. 10 + 20 = 30 Coins.
b. 5x + 20y = 5*10 + 20*20 = 450 Cents = $4.50.
c. 5x + 10y = 5*10 + 10*20 = 250 Cents = $2.50.
a) 10 nickels; 20 dimes
b) $4.50 (10 nickels; 40 dimes)
c) $2.50
To model the problem using Singapore Math, we can use a bar model, also known as a tape diagram or a part-whole diagram. Let's solve the problem step by step:
Step 1: Define the variables and assign them numbers:
- Let x represent the number of nickels Zachary saved.
- Let y represent the number of dimes Zachary saved.
- Let z represent the number of nickels Lily saved. (Note: We'll express all quantities related to Lily's savings in terms of Zachary's savings.)
- Since Lily saved 2y dimes, the number of dimes Lily saved is 2y.
- Since the total number of her dimes is 4 times the total number of her nickels, we can express it as 4z.
With this information, we can create the following bar model:
Zachary's Savings Lily's Savings
---------------------------------------------------------
| |
| |
| | |
| | |
| x nickels | z nickels |
| | |
| | |
|-----------------------------------------|
| | |
| | |
| y dimes | 2y dimes |
| | |
| | |
---------------------------------------------------------
Step 2: Write the given conditions as mathematical expressions:
- Lily saved $2 more than Zachary, so her savings can be represented as x + 2.
- The total number of Lily's dimes is 4 times the total number of her nickels, so 2y = 4z.
Step 3: Solve the problem using the equations:
- Since Lily saved $2 more than Zachary, we can set up the equation: z + 2 = x.
- The total number of her dimes is 4 times the total number of her nickels, so we can set up the equation: 2y = 4z.
To solve for a, b, and c, we need to solve this system of equations. However, since the specific values of x and y are not given, the solution will be in terms of x and y.
a) How many coins does Zach have?
Since Zach saved x nickels and y dimes, the total number of coins he saved is x + y.
b) How much did Lily save?
Since the value of each nickel is 0.05 and the value of each dime is 0.10, we can represent Lily's savings as: (0.05z) + (0.10 * 2y)
Since she saved $2 more than Zachary: (0.05z) + (0.10 * 2y) = (0.05x + 0.10y) + 2
Simplifying further, we can express Lily's savings as: 0.05z + 0.20y = 0.05x + 0.10y + 2
c) How much did Zachary save?
Since he saved x nickels and y dimes, we can represent Zachary's savings as: (0.05x) + (0.10y)
To find the specific values of a, b, and c, we would need the exact values of x and y. However, this modeling approach illustrates the relationship between their savings and formulas to calculate them.