Question
Small boxes contain DVDs, and large boxes contain one gaming machine. Three boxes of gaming machines and a box of DVDs weight 48 pounds. Three boxes of gaming machines and five boxes of DVDs weight 72 pounds. How much does each box weigh?
Answers
Bot
Let's call the weight of a box of DVDs "x" and the weight of a box containing a gaming machine "y."
From the first sentence, we know that:
- Each small box (containing DVDs) weighs x
- Each large box (containing a gaming machine) weighs y
From the second sentence, we know that:
- 3 large boxes + 1 small box weigh 48 pounds, or 3y + 1x = 48
- 3 large boxes + 5 small boxes weigh 72 pounds, or 3y + 5x = 72
We can use these two equations to solve for x and y. Here's one way to do it:
1. Rearrange the first equation to solve for x:
1x = 48 - 3y
2. Substitute this expression for x into the second equation:
3y + 5(48 - 3y) = 72
3. Simplify and solve for y:
3y + 240 - 15y = 72
-12y = -168
y = 14
4. Plug this value of y back into either equation to find x:
3(14) + 1x = 48
x = 6
So each box of DVDs weighs 6 pounds, and each box containing a gaming machine weighs 14 pounds.
From the first sentence, we know that:
- Each small box (containing DVDs) weighs x
- Each large box (containing a gaming machine) weighs y
From the second sentence, we know that:
- 3 large boxes + 1 small box weigh 48 pounds, or 3y + 1x = 48
- 3 large boxes + 5 small boxes weigh 72 pounds, or 3y + 5x = 72
We can use these two equations to solve for x and y. Here's one way to do it:
1. Rearrange the first equation to solve for x:
1x = 48 - 3y
2. Substitute this expression for x into the second equation:
3y + 5(48 - 3y) = 72
3. Simplify and solve for y:
3y + 240 - 15y = 72
-12y = -168
y = 14
4. Plug this value of y back into either equation to find x:
3(14) + 1x = 48
x = 6
So each box of DVDs weighs 6 pounds, and each box containing a gaming machine weighs 14 pounds.