A charity organization is collecting change to raise money. They have collected three times as many dimes as quarters, 11 more nickels than dimes, and 2 times as many pennies as nickels.
Let x represent the number of quarters. Write an expression to represent the number of dimes.
Write an expression to represent the number of nickels.
Write an expression to represent the number of pennies.
If they have collected a total of 4,453 coins, how many of each coin have they collected?
No... that is absolutely wrong.
p = 2n
n = d+11
d = 3x
n = 3x+11
p = 2(3x+11) = 6x+22
p+n+d+x = 4453
6x+22 + 3x+11 + 3x + x = 4453
13x + 33 = 4453
13x = 4420
x = 340
So, we have
340 quarters
1020 dimes
1031 nickels
2062 pennies
check: 340+1020+1031+2062 = 4453
Is this for connections academy?
Well, let's put on our mathematical clown nose and get started!
To represent the number of dimes, we can use the expression "3x". Since they have collected three times as many dimes as quarters, the number of dimes is three times the number of quarters, which is represented by "x".
Next, let's move on to the nickels. The expression for the number of nickels would be "(3x + 11)". This is because there are 11 more nickels than dimes, which is represented by "3x".
Lastly, we have the pennies. The expression for the number of pennies would be "2(3x + 11)". This is because there are 2 times as many pennies as nickels, which is represented by "3x + 11".
Now that we have our expressions, let's solve the problem!
If they have collected a total of 4,453 coins, we can set up the equation:
x + 3x + (3x + 11) + 2(3x + 11) = 4453
Now we have an equation to solve. Remember, I'm a clown bot and I'm not too good at math, but I'll do my best!
Simplifying the equation, we get:
x + 3x + 3x + 11 + 6x + 22 = 4453
13x + 33 = 4453
Subtracting 33 from both sides:
13x = 4420
Dividing both sides by 13:
x = 340
Now we know that x, representing the number of quarters, is 340. Let's plug that value back into our expressions to find the number of each coin:
Number of dimes: 3x = 3(340) = 1020
Number of nickels: 3x + 11 = 3(340) + 11 = 1031
Number of pennies: 2(3x + 11) = 2(1031) = 2062
So, they have collected 340 quarters, 1020 dimes, 1031 nickels, and 2062 pennies.
Hope that brings a chuckle to your math problem!
To write expressions to represent the number of each coin, let's break down the given information step by step:
1. Dimes: The charity organization has collected three times as many dimes as quarters. Let's use x to represent the number of quarters. Therefore, the number of dimes can be expressed as 3x.
2. Nickels: The organization has collected 11 more nickels than dimes. Using the expression we found in step 1 (3x) for the number of dimes, the expression for the number of nickels will be 3x + 11.
3. Pennies: The organization has collected 2 times as many pennies as nickels. Using the expression we found in step 2 (3x + 11) for the number of nickels, the expression for the number of pennies will be 2(3x + 11), which simplifies to 6x + 22.
Now that we have expressions for the number of each coin, let's solve the problem with the given total number of coins.
The given information states that the total number of coins collected is 4,453. We can set up an equation using the expressions we found:
x (quarters) + 3x (dimes) + (3x + 11) (nickels) + (6x + 22) (pennies) = 4,453
Simplifying this equation, we have:
13x + 33 = 4,453
Now, we can solve for x:
13x = 4,453 - 33
13x = 4,420
x = 4,420 / 13
x ≈ 340
So, the number of quarters (x) is approximately 340.
From here, we can substitute this value back into our expressions to find the number of each coin:
Dimes = 3x = 3 * 340 = 1,020
Nickels = 3x + 11 = 3 * 340 + 11 = 1,031
Pennies = 6x + 22 = 6 * 340 + 22 = 2,062
Therefore, the charity organization has collected approximately 340 quarters, 1,020 dimes, 1,031 nickels, and 2,062 pennies.
In one physical education class, 5/8 of the students were playing basketball. After 3 more students joined, 18 students were playing basketball. Which equation represents how many students are in the class?
a. X Quarters.
b. 2x Dimes.
(2x+22) Nickels.
3(2x+22) Pennies.
c. X + 2x +(2x+22) + 3(2x+22)=2134.
X + 2x + 2x + 22 + 6x + 66 = 2134
11x + 88 = 2134
11x = 2046
X = 186 Quarters.
2x = 2*186 = 372 Dimes.
2x+22 = 372 + 22 = 394 Nickels.
3(2x+22) = 3 * 394 = 1182 Pennies.