Help me please

Question

A bow and arrow cost £24. The bow costs £19 more than the arrow. Make two equations and solve them to find the cost of a bow and arrow. Use a to represent the arrow and b to represent the bow.

 

This is confusing me to no end but I need to do it and get it right because it counts to a quarter of my homework.

Answer 1

This is how I would approach the problem:

1. You know that an arrow and a bow together are $24 (i'm just going to use the dollar sign for now)
1. so if an arrow is a and a bow is b you have: a + b = 24. That would be the first equation
2. Then you know a bow is $19 more than an arrow. So the equation for that would be:
1. b = a + 19
3. Next I would put the equation from part 2 into the first equation and solve for a
1. a + (a + 19) = 24 you can drop the parenthesis in this case
2. 2a + 19 = 24
3. 2a = 5
4. a = 5/2 or 2.5 is the cost of an arrow
4. you can take that solution and plug it into either equation to solve for the cost of the bow, b
1. 2.5 + b = 24 or b = 2.5 + 19
2. when you solve you get b = $21.5

Answer 2

Let a = the cost of the arrow in pounds sterling

Let b = the cost of the bow in pounds sterling

 

We have 2 unknowns (a and b) so we need two equations relating them:

 

A bow and arrow cost £24:  a + b = 24

The bow costs £19 more than the arrow: b = a + 19

 

The second equation tells us that b=19+a.  So let's substitute 19+a in place of b in the first equation:

a + b = 24

a + 19 + a = 24

2a = 5

a = 2.5 pounds sterling

 

Solve for b, the bow:

b = 19 + a

b = 19 + 2.5 = 21.5 pounds sterling

 

Check:

a + b = 24

2.5 + 21.5 = 24

24 = 24        CHECK!

 

JOLLY GOOD!