Your math teacher tells you that the next test is worth 100 points and contains 38 problems. multiple choice questions are worth 2 points each and word problems are 5 points. how many of each type are there

30 multiple choice questions and 8 word problems

Step-by-step explanation:

Let m = number of multiple choice questions.

Let w = number of word problems.

There are 38 problems altogether, so we have the first equation concerning the number of problems.

m + w = 38

A multiple choice question is worth 2 points, so m multiple choice questions are worth 2m points. A word problem is worth 5 points, so w word problems are worth 5w points. Altogether, both types of problems are worth 2m + 5w points. We are told all problems combined are worth 100 points. We can now write our second equation concerning the number of points.

2m + 5w = 100

We have a system of two equations in two unknowns.

m + w = 38

2m + 5w = 100

We can use the substitution method to solve the system of equations.

Solve the first equation for m.

m + w = 38

Subtract w from both sides.

m = 38 - w

Now where we see m in the second original equation, we substitute it with 38 - w.

The second original equation is

2m + 5w = 100

Substitute 38 - w for m in the equation.

2(38 - w) + 5w = 100

We have a single equation in a single variable, so we can solve it for the variable.

Distribute the 2.

76 - 2w + 5w = 100

Combine like terms on the left side.

76 + 3w = 100

Subtract 76 from both sides.

3w = 24

Divide both sides by 3.

w = 8

There are 8 word problems.

Now we use the first original equation and substitute 8 for w and solve for m.

m + w = 38

m + 8 = 38

Subtract 8 from both sides.

m = 30

There are 30 multiple choice questions.

30 multiple choice questions and 8 word problems

Check:

30 questions + 30 problems = 38 problems in total

30 questions @ 2 pts each = 2 * 30 pts = 60 pts

8 problems @ 5 pts each = 5 * 8 pts = 40 pts

60 pts + 40 pts = 100 pts

The total is 38 problems and 100 points, so our answer is correct.

walter needs to make at least 5 more cookies but no more than 40. 5 ≥ x ≥ 40;

step-by-step explanation:

walter has to make a minimum of 20 cookies. he already has 15 cookies made, so he must make 5 more to meet the minimum.

the maximum amount of cookies he can make is 55. he already has 15, so he has to make no more than 40 more cookies to meet the maximum.