Susan wants to use blue, yellow, green, and pink paint to decorate her house. She needs 3 times as much blue paint as yellow paint and 1/2 as much yellow paint as green paint. She needs 3 1/4 gallons of pink paint, which is 3/4 of a gallon more than the green paint she needs. How much paint does Susan need in all?
Is the answer 10 3/4?
To find the answer, we need to calculate the amount of each color of paint Susan needs and then add them together.
Let's start with the green paint:
Let's assume the amount of green paint Susan needs is G gallons.
According to the given information, Susan needs 3/4 gallon less than the pink paint, which is 3 1/4 gallons. So, the green paint Susan needs can be calculated as:
G = 3 1/4 - 3/4 = 3 gallons.
Next, let's move on to the yellow paint:
We know that Susan needs half as much yellow paint as green paint. So, the amount of yellow paint Susan needs can be calculated as:
Y = G/2 = 3/2 = 1.5 gallons.
Now, let's calculate the blue paint:
We are given that Susan needs 3 times as much blue paint as yellow paint. So, the amount of blue paint Susan needs can be calculated as:
B = 3 * Y = 3 * 1.5 = 4.5 gallons.
Finally, let's calculate the amount of paint Susan needs in total:
Total = Pink + Green + Yellow + Blue
Total = 3 1/4 + 3 + 1.5 + 4.5
Total = 3.25 + 3 + 1.5 + 4.5
Total = 12.25 gallons.
Therefore, Susan needs a total of 12.25 gallons of paint for her house. So, the answer is NOT 10 3/4; it is 12 1/4 gallons or 12.25 gallons.
To find out how much paint Susan needs in total, we need to calculate the amount of each color of paint.
Let's start by assigning variables to the unknown amounts of paint:
Let's say the amount of yellow paint Susan needs is Y.
Then, the amount of blue paint she needs is 3 times that, so it is 3Y.
The amount of green paint she needs is G, and the amount of pink paint she needs is 3 1/4 gallons.
Next, let's use the given information to create equations:
1) Susan needs 3 times as much blue paint as yellow paint, so we can write the equation:
Blue paint = 3 times yellow paint
3Y = 3Y
2) Susan needs 1/2 as much yellow paint as green paint, so we can write the equation:
Yellow paint = 1/2 times green paint
Y = 1/2 G
3) Susan needs 3 1/4 gallons of pink paint, which is 3/4 of a gallon more than the green paint she needs, so we can write the equation:
Pink paint = Green paint + 3/4
3 1/4 = G + 3/4
To solve these equations, we can substitute equation 2 and 3 into equation 1 to find the values of Y, G, and Pink paint:
3Y = 3Y (equation 1)
Y = 1/2 G (equation 2)
3 1/4 = G + 3/4 (equation 3)
Rearrange equation 2 for G:
G = 2Y (equation 4)
Substitute equation 4 into equation 3:
3 1/4 = 2Y + 3/4
To solve this equation, we need to remove the fractions:
3 1/4 = 8/4Y + 3/4
3 1/4 = 11/4Y
Now, let's convert the mixed number (3 1/4) into an improper fraction:
3 1/4 = (4*3 + 1)/4 = 13/4
Substitute the value of 3 1/4 in equation 3:
13/4 = 11/4Y
Now, solve for Y:
13Y = 11
Y = 11/13
Substitute the value of Y in equation 4:
G = 2 * (11/13) = 22/13
Substitute the value of G in equation 2:
Y = 1/2 * (22/13) = 22/26 = 11/13
Now, substitute the values of Y and G into equation 1:
3Y = 3 * (11/13) = 33/13
Lastly, calculate the total amount of paint Susan needs:
Total paint = Yellow paint + Blue paint + Green paint + Pink paint
Total paint = (11/13) + (33/13) + (22/13) + (13/4)
Common denominators of 13 and 4 will be 52:
Total paint = (44/52) + (132/52) + (88/52) + (169/52)
Total paint = 433/52
The answer is not exactly 10 3/4 gallons but 433/52 gallons.