word problem : a couple needed to purchase 21 presents for christmas presents. if the husband bought twice as many as his wife, how many did each buy?

Question

I wanted to try and use this formula but wanted to see if I was on the right track. X(2)+y=21

Answer 1

These word problems are always the toughest. The first sentence is always the one that will cause the wrong answer.

 

Let's look at the first sentence: " a couple needed to purchase 21 presents for Christmas"

 

So in Math language that would mean: [husband's presents] + [wife's presents]= 21. Simple enough.

 

Let's look at the second sentence: "if the husband bought twice as many as his wife, how many did each buy?"

 

This is where it gets tricky. Now our variables change to: 2[wife's presents] + [wife's presents]=21.

 

So if we gave the variables h for the husband and w for the wife, our equation would now look like:

 

h + w = 21

 

but now we know that the husband's presents equal twice as many as his wife. Therefore we can replace h with 2w and then solve for w. 

 

2w + w =21

 

Luckily, we can solve for w now and then solve the entire equation. I'll give the answer further down below, in case you want to work on it yourself.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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So with our new equation we can solve for w.

 

 

2w + w= 21

 

3w=21

 

w=7

 

 

So the wife bought 7 presents, now we can plug that into our first equation.

 

h + 7=21

 

h= 14

 

Now our answer is:

 

The wife bought 7 presents and the husband bought 14 presents.