I am having trouble with this math Mixture problem.
shirley has a quantity of yellow tulip bulbs worth .10 cents each, pink tulip bulbs worth .20 cents each and red tulip bulbs worth .25 cents each. In her total collection of bulbs, there are five more pink bulbs than yellow bulbs and twice as many red bulbs as the sum of the other two kinds. if the bulbs altogether are worth $133.50 how many of each kind does shirley have.
p = y+5
r = 2(p+y)
10y+20p+25r = 13350
100 yellow, 105 pink, and 410 red. Thank you so much this really help
Looks like Shirley's garden is really blooming with tulip bulbs! But let's hold our horses and solve this math problem, shall we?
Let's start by assigning variables:
Let Y be the number of yellow tulip bulbs.
Since there are five more pink bulbs than yellow bulbs, let P be Y + 5 (the number of pink bulbs).
Since there are twice as many red bulbs as the sum of the other two kinds, let R be 2(Y + P) (the number of red bulbs).
Now, let's calculate the value of each type of bulb:
Yellow bulbs are worth $0.10, so the value of the yellow bulbs is 0.10Y.
Pink bulbs are worth $0.20, so the value of the pink bulbs is 0.20P.
Red bulbs are worth $0.25, so the value of the red bulbs is 0.25R.
According to the problem, the total value of all the bulbs is $133.50, so we can set up the equation:
0.10Y + 0.20P + 0.25R = 133.50
Now let's substitute the values of P and R:
0.10Y + 0.20(Y + 5) + 0.25(2(Y + 5)) = 133.50
Simplifying this equation, we get:
0.10Y + 0.20Y + 1 + 0.50Y + 2.50 = 133.50
0.80Y + 3.50 = 133.50
0.80Y = 130
Y = 130 / 0.80
Y ≈ 162.50
Uh-oh! It seems like we got a decimal value for the number of yellow tulip bulbs, which doesn't make sense. There might be an error in the problem description or the calculations I did.
But hey, don't worry! Sometimes math problems can be a bit tricky, like a juggling act gone wrong. It's always a good idea to double-check the problem and try solving it step by step.
Let's break down the problem step by step:
Step 1: Define the variables
Let's define the variables:
Let "x" be the number of yellow tulip bulbs.
Therefore, the number of pink tulip bulbs is "x + 5" (five more pink bulbs than yellow bulbs).
And the number of red tulip bulbs is "2(x + (x + 5))" (twice as many red bulbs as the sum of the other two kinds).
Step 2: Convert the bulb prices
The price of yellow tulip bulbs is $0.10 each.
The price of pink tulip bulbs is $0.20 each.
The price of red tulip bulbs is $0.25 each.
Step 3: Write the equation for the total value
The total value of the bulbs is given as $133.50.
So, we can write the equation:
(x * $0.10) + ((x + 5) * $0.20) + (2(x + (x + 5))) * $0.25 = $133.50
Step 4: Solve the equation
Now, let's solve the equation:
0.10x + 0.20(x + 5) + 0.25(2(x + (x + 5))) = 133.50
0.10x + 0.20x + 1 + 0.25(4x + 10) = 133.50
0.10x + 0.20x + 1 + 4x + 2.50 = 133.50
Combine like terms:
4.30x + 3.50 = 133.50
4.30x = 130
Divide both sides by 4.30:
x = 30
Step 5: Calculate the number of each type of bulb
Now that we have the value of "x," we can substitute it back into our variables to find the number of each type of bulb:
Yellow tulip bulbs:
x = 30
Pink tulip bulbs:
x + 5 = 30 + 5 = 35
Red tulip bulbs:
2(x + (x + 5)) = 2(30 + (30 + 5)) = 2(30 + 35) = 2(65) = 130
Therefore, Shirley has 30 yellow tulip bulbs, 35 pink tulip bulbs, and 130 red tulip bulbs.
To solve this math mixture problem, we can set up a system of equations based on the given information.
Let's call the number of yellow tulip bulbs Y, the number of pink tulip bulbs P, and the number of red tulip bulbs R.
From the problem, we know the following information:
1. The value of each yellow tulip bulb is $0.10, so the total value of the yellow bulbs is 0.10 * Y.
2. The value of each pink tulip bulb is $0.20, so the total value of the pink bulbs is 0.20 * P.
3. The value of each red tulip bulb is $0.25, so the total value of the red bulbs is 0.25 * R.
4. There are five more pink bulbs than yellow bulbs: P = Y + 5.
5. There are twice as many red bulbs as the sum of the other two kinds: R = 2 * (0.10 * Y + 0.20 * P).
Now, we can set up the equation for the total value of the bulbs:
0.10 * Y + 0.20 * P + 0.25 * R = $133.50.
We also have the two additional equations from the given information:
P = Y + 5, and R = 2 * (0.10 * Y + 0.20 * P).
Now, we can substitute the values of P and R in terms of Y into the equation for the total value of the bulbs to get a single equation in terms of Y:
0.10 * Y + 0.20 * (Y + 5) + 0.25 * (2 * (0.10 * Y + 0.20 * (Y + 5))) = $133.50.
Simplifying this equation will give us the value of Y, and then we can use that value to find the values of P and R using the equations P = Y + 5 and R = 2 * (0.10 * Y + 0.20 * P).
You can now solve this equation to find the values of Y, P, and R. Remember to double-check your solution by plugging the values back into the original equations to make sure they all hold true.