1/4 of henry sticker is equal to 2/3 of daisy. difference in number of sticker each of them has is 135. how many stickers do they have in all?
Let x = Daisy stickers
Let y = Henry stickers
According to the problem:
(1/4)y = (2/3)x
And understanding the first statement, we can say that Henry has more stickers than Daisy:
y - x = 135
Substituting the second equation to first (with y = 135 + x);
(1/4)(135 + x) = (2/3)x
[ (1/4)(135 + x) = (2/3)x ] * 12
3(135 + x) = 8x
405 + 3x = 8x
405 = 5x
x = 81 stickers (Daisy)
y = 135+x = 216 stickers (Henry)
hope this helps~ `u`
Well, it seems like Henry and Daisy are a pretty dynamic duo with their sticker collection! To solve this math problem, let's break it down into smaller bits, just like dividing a sticker in half.
So, if 1/4 of Henry's stickers is equal to 2/3 of Daisy's stickers, that means we can set up an equation like this:
(1/4) * H = (2/3) * D
Now, the problem tells us that the difference in the number of stickers each of them has is 135. So, we can set up another equation:
H - D = 135
Now comes the fun part - solving these equations! But hey, don't worry, I'll handle the math for you.
Multiplying the first equation by 12 to clear the fractions, we get:
3H = 8D
Now, let's solve the system of equations using substitution.
From the second equation, we can solve it for H:
H = D + 135
Now, substitute H in the first equation with the expression (D + 135):
3(D + 135) = 8D
Expanding and simplifying, we get:
3D + 405 = 8D
Subtracting 3D from both sides:
405 = 5D
Dividing both sides by 5:
D = 81
Now that we know Daisy has 81 stickers, we can find Henry's number of stickers using the second equation:
H = D + 135
H = 81 + 135
H = 216
So, Henry has 216 stickers!
Now we add their totals together to find out how many stickers they have in total:
Henry (H) + Daisy (D) = 216 + 81 = 297
So, in total, they have 297 stickers. They sure love their stickers!
Let's break down the problem into steps:
Step 1: Let's assume that Henry has x stickers.
Step 2: According to the problem, 1/4 of Henry's stickers is equal to 2/3 of Daisy's stickers. This can be written as:
(1/4)x = (2/3)y, where y is the number of stickers Daisy has.
Step 3: The problem also states that the difference in the number of stickers each of them has is 135. This can be written as:
x - y = 135
Step 4: Now, we can solve the system of equations from Step 2 and Step 3 to find the values of x and y. Multiply both sides of equation 1 by 12 and equation 2 by 3 to eliminate the fractions:
3x = 8y (equation 3)
12x - 12y = 16200 (equation 4)
Step 5: Solve equation 3 for x:
x = (8/3)y
Step 6: Substitute the value of x in equation 4:
12(8/3)y - 12y = 16200
96y - 36y = 16200
60y = 16200
y = 16200/60
y = 270
Step 7: Substitute the value of y back into equation 3 to solve for x:
3x = 8(270)
3x = 2160
x = 2160/3
x = 720
Step 8: Now we know that Henry has 720 stickers and Daisy has 270 stickers.
Step 9: To find the total number of stickers they have in all, we add their quantities:
720 + 270 = 990
Therefore, they have a total of 990 stickers.
To solve this problem, we need to set up equations based on the given information and then solve for the number of stickers each person has.
Let's assume Henry has "x" number of stickers and Daisy has "y" number of stickers.
According to the first statement, 1/4 of Henry's stickers is equal to 2/3 of Daisy's stickers:
(1/4) * x = (2/3) * y
Now we know that the difference in the number of stickers between Henry and Daisy is 135:
x - y = 135
To solve these equations, we can use the method of substitution or elimination. In this case, let's solve using substitution.
From the first equation, we can isolate "x" by multiplying both sides by 4:
x = (2/3) * 4y
x = (8/3) * y
Now substitute this value of "x" into the second equation:
(8/3) * y - y = 135
To get rid of the fraction, we can multiply everything by 3:
8y - 3y = 405
5y = 405
Divide both sides by 5 to solve for "y":
y = 405 / 5
y = 81
Now substitute the value of "y" back into the first equation to find "x":
x = (8/3) * 81
x = 216
Therefore, Henry has 216 stickers and Daisy has 81 stickers.
To find the total number of stickers, we can simply add their quantities:
216 + 81 = 297
So, they have a total of 297 stickers.