Solving systems of equations word problems worksheet for all problems, define variables, write the system of equations and solve variables.

Question

At a restaurant, the cost for a breakfast taco and a small glass of milk is $2.10. the cost for 2 tacos and 3 small glasses of milk is $5.15. Which pair of equations can be used to determine t, the cost of a taco, and m, the cost of a small glass of milk?

Answer 1

Answer 2

The first step is to write the information as two equations. The variables are given to us as t₁ = cost of a taco

and m₁ = cost of a glass of milk.

In the information for both equations we're given the number of items purchased. For the first a single taco and glass of milk costs $2.10, therefore

t₁ + m₁ = $2.10

For the second equation we're given the cost of 2 tacos and 3 glasses of milk equals $5.15, therefore

2t₁ + 3m₁ = $5.15

If we want to solve for the values of t₁ and m₁, we need to write an equation which defines one variable in terms of the other. We can do this by subtracting one equation from the other.

2t₁ + 3m₁ = $5.15

-(t₁ + m₁) = $2.10

t₁ + 2m₁ = $3.05

Next solve for t₁ by subtracting m₁ from both sides of the equation

t₁ + 2m₁ = $3.05

-2m₁ -2m₁

t₁ = $3.05 - 2m₁

To solve for the first variable, $3.05 - 2m₁ can be substituted for t₁ in either equation

t₁ + m₁ = $2.10

($3.05 - 2m₁) + m₁ = $2.10

Combine like terms to get

$3.05 - m₁ = $2.10

Subtract $3.05 from both sides of the equations

-m₁ = -$0.95

Multiply both sides by -1 to solve for m_1, which results in

m₁ = $0.95

Now it's possible to solve for t₁ by putting the value of m₁ into the equation for t₁

t₁ = $3.05 - 2m₁

t₁ = $3.05 - 2($0.95)

t₁ = $3.05 - $1.90

t₁ = $1.15

Now check the answer by substituting the values of t₁ and m₁ into both equations

t₁ + m₁ = $2.10

$1.15 + $0.95 = $2.10

2t₁ + 3m₁ = $5.15

2($1.15) + 3($0.95) = $5.15

$2.30 + $2.85 = $5.15

Both equations are true so we have found the correct values. Hope this helps!

Answer 3

Variables:

t: cost of taco

m: cost of milk

1 taco and 1 glass of milk cost $2.10, so:

t + m = 2.10

2 tacos and 3 glasses of mil cost $5.15, so:

2t + 3m = 5.15

The system of equations is:

t + m = 2.10

2t + 3m = 5.15

Solve system of equations:

t + m = 2.10

m = 2.10 - t

replacing m into the second equation:

2t + 3 (2.10 - t) = 5.15

2t + 6.3 - 3t = 5.15

-1t + 6.3 = 5.15

-t = 5.15 - 6.3

-t = -1.15

t = 1.15

replacing t into the first equation:

1.15 + m = 2.10

m = 2.10 - 1.15

m = 0.95

The cost of a taco is $1.15 and the cost of a glass of milk is $0.95