luke had 135 sticky labels, vicente had 990 sticky labels, and Haley had 570 sticky labels. after haley gave an equal number of sticky labels to both boys, vicente had 4 times as many sticky labels as luke. how many sticky labels did haley have?
990+x = 4(135+x)
x = 150
So, haley had 570-2x = 270
Well, it seems like Haley is the real label queen here! Let's solve this sticky situation together.
Let's assume that Haley gave x sticky labels to both Luke and Vicente. After Haley shared her sticky love, Luke was left with (135 + x) labels, and Vicente was left with (990 + x) labels.
According to the problem, Vicente ended up with 4 times as many sticky labels as Luke, so we can set up the equation:
4(135 + x) = 990 + x
Now let's solve for x. *cue suspenseful music*
540 + 4x = 990 + x
Combining like terms:
3x = 450
Dividing both sides by 3:
x = 150
So Haley shared 150 sticky labels with both Luke and Vicente. Now let's find out how many labels Haley had left.
Haley started with 570 sticky labels and gave away 150 labels:
570 - 150 = 420
Haley was left with 420 sticky labels, proving that she's still the sticky label queen!
Let's start by finding the number of sticky labels each person has after Haley gave an equal number to Luke and Vicente.
Let's assume the number of sticky labels Haley gave to Luke and Vicente is "x".
After Haley gave "x" sticky labels to Luke:
Luke's new count = 135 + x
After Haley gave "x" sticky labels to Vicente:
Vicente's new count = 990 + x
According to the given information, Vicente had 4 times the number of sticky labels as Luke after receiving the equal amount from Haley:
4(Luke's new count) = Vicente's new count
Let's substitute the values:
4(135 + x) = 990 + x
Now, we can solve the equation to find the value of "x" and then calculate the number of sticky labels that Haley had initially.
4(135 + x) = 990 + x
540 + 4x = 990 + x
4x - x = 990 - 540
3x = 450
x = 450/3
x = 150
So, Haley gave 150 sticky labels to both Luke and Vicente.
Now, let's find how many sticky labels Haley had initially:
Haley's initial count = Haley's count - x
Haley's initial count = 570 - 150
Haley's initial count = 420
Therefore, Haley initially had 420 sticky labels.
To solve this problem, let's break it down step by step:
1. Let's represent the number of sticky labels Luke had after receiving from Haley as "x".
2. Since Vicente had 4 times as many sticky labels as Luke, we can represent the number of sticky labels Vicente had after receiving from Haley as "4x".
3. Before Haley gave her sticky labels to the boys, the total number of sticky labels was the sum of the quantities each person had: 135 + 990 + 570 = 1695.
4. After Haley gave an equal number of sticky labels to both boys, Luke had x sticky labels and Vicente had 4x sticky labels. So, the total number of sticky labels becomes x + 4x = 5x.
5. We know that the total number of sticky labels after Haley's distribution is 1695, so we can write the equation: 5x = 1695.
6. To solve for x, we divide both sides of the equation by 5: x = 1695 / 5 = 339.
Therefore, Haley gave 339 sticky labels to both Luke and Vicente.
To find out how many sticky labels Haley had initially, we need to subtract the number she gave away from the total she had before giving any to the boys:
Haley's initial quantity = Haley's remaining quantity + Sticky labels given to Luke + Sticky labels given to Vicente
= 570 + 339 + 339
= 1248.
Haley initially had 1248 sticky labels.