Twin Jose and HoseB have a combined weight of 430 pounds. HoseB is 58 pounds heavier than Jose. How much does each weigh?

Question

I need 2 equations so I can solve using elimination or substitution.

Answer 1

A+B=430

B=A+58

2 equations, 2 unknowns

substitute 2nd into the 1st

A+B =430

A + A+58 =430

2A = 430 -58 = 372

2A = 372

A =372/2 = 186

B = A+58 = 186 + 58 = 244

Answer 2

Step 1: Define your variables, or unknowns. In this question, there are two equations and two unknowns. It is important to define what your unknowns are before you start.

Unknowns (or variables):

j = Jose's weight

h = HoseB's weight

Step 2: Find your two equations using the information in the question

The first sentence tells you that they have a combined weight of 430 pounds. So equation #1 is:

j + h = 430

The second sentence says that HoseB is 58 pounds heavier than Jose. So equation #2 is:

h = j + 58

Step 3: Now we have our two equations. To solve for the variables, we can either use substitution or elimination. You can choose either method, but I will explain both here.

3a. Substitution:

Since equation #2 has one variable on its own, we can easily use substitution. We know h = j + 58, so we can substitute for h in equation #1.

Eq #1 with h substitution: j + (j + 58) = 430

Now this equation only has 1 variable, and we can solve for j

Remove Parenthesis:

j + j + 58 = 430

Combine like terms:

2j + 58 = 430

Subtract 58 from both sides:

2j = 372

Divide both sides by 2:

j = 186

Now that we solved for j, we can plug it in to either equation that we started with to solve for h:

I will use equation #2:

h = j + 58

h = 186 + 58

h = 244

3b. Elimination:

To use elimination, you first line up the 2 equations with both variables on one side of the equals (need to rearrange equation #2).

Eq #1: h + j = 430

Eq #2: h - j = 58

Now you can either add or subtract the two equations. The goal is to eliminate one of the variables so that there is only one unknown left that we can solve for. Since we see a +j in eq #1 and -j in eq #2 we can easily eliminate the j variable by adding the two equations (+ j - j = 0).

So when we add the equations down each column we get:

h + j = 430

h - j = 58

2h + 0 = 488

Now solve:

2h = 488

h = 244

Now plug h into either equation to solve for j.

h + j = 430

244 + j = 430

j = 186

As you can see, the two methods give you the same answers.