System of equation word problems may seem tricky at first, but I will walk you through step by step.
Let’s say that you get the following word problem.
The price of a backpack and a purse combined equals $60. The price of the backpack is three times than the price of the purse.
In this system, we will have b represent the cost of the backpack, and p represent the cost of the purse.
First of all we see that b and p combined makes 60. This gives us our first equation.
b+p=60
We also see the b is three times the cost of p. We can write that like this.
b=3p
Now we have our system of equations.
b+p=60 b=3p
Now the best way to solve is to find out what p equals first. If we do so, we plug it into the second equation to find b.
How can we find what p is, though? In the first equation we know that whatever b is + p will give us 60. In the second equation, b=3p. In the first equation we can replace b with the information in the second equation that shows what it is equivalent to.
3p+p=60 4p=60 p=60/4 p=15
Now we know that the purse cost 15$. We also know that the backpack cost 3 times that, as written in the second equation. 15(3)=45, so now we have our values.
The backpack costed $45, and the purse costed $15.
I hope this explanation was clear enough and that it helped!
