Question 1

Bill earned 3 times as much as Jim one weekend. Tom earned $$5 more than Jim. If together they earned 90$$, how much did each person earn?

Accepted Answer

$$\15$ for Jim, $$\$$45$$ for Bill, $$\20$ for Tom

Question 2

The lengths of the sides of a triangle are represented by three consecutive integers. If the perimeter of the triangle is $$18$$ feet, what are the lengths of its sides?

Accepted Answer

$$5 ft$$, $$6 ft$$, $$7 ft$$

Question 3

A child sells lemonade at $$\2$ per cup, then increases the price to $$\$$3$$ per cup. She sells all $$50$$ cups and earns $$\124$. If x$ is the number of cups sold at $$\$$2$$ each, which equation models the situation?

Accepted Answer

$$2x + 3(50 - x) = 124$$

Question 4

Using the equation $$2x + 3(50 - x) = 124$$, how many cups did the child sell at $$\2$ each?

Accepted Answer

$$26$$

Question 5

If the child sold $$x$$ cups at $$\2$ and y$ cups at $$\$$3$$, and sold all $$50$$ cups for $$\124$, what is the value of y$?

Accepted Answer

$$24$$

Question 6

If the sides of a triangle are $$x$$, $$x+1$$, and $$x+2$$ and the perimeter is $$18$$, what is the value of $$x$$?

Accepted Answer

$$5$$

Question 7

Suppose Tom earned $$5$$ more than Jim, and Bill earned $$3$$ times as much as Jim. If their total earnings were $$90$$, which equation represents the situation?

Accepted Answer

$$x + 3x + (x + 5) = 90$$

Question 8

If Jim earned $$x$$ dollars, Bill earned $$3x$$ dollars, and Tom earned $$x+5$$ dollars, what is the value of $$x if $$their total earnings were $$90$$?

Accepted Answer

$$15$$

Question 9

A triangle has sides of lengths $$x$$, $$x+1$$, and $$x+2. If $$the perimeter is $$18$$ feet, what is the length of the longest side?

Accepted Answer

$$7 ft$$

Question 10

A child sells $$x$$ cups of lemonade at $$\2$ each and 50-x$ cups at $$\$$3$$ each, earning $$\124$ in total. What is the value of x$?

Accepted Answer

$$26$$

Question 11

If a triangle has sides $$x$$, $$x+1$$, $$x+2$$ and the perimeter is $$18$$, what is the sum of the lengths of the two shortest sides?

Accepted Answer

$$11 ft$$

Question 12

If Bill earned $$3$$ times as much as Jim, and Tom earned $$5$$ more than Jim, which expression represents Tom's earnings?

Accepted Answer

$$x + 5$$

Question 13

A child sells $$x$$ cups at $$\2$ and y$ cups at $$\$$3$$, with $$x + y = 50$$ and $$2x + 3y = 124. $$What is the value of $$y$$?

Accepted Answer

$$24$$

Question 14

If the perimeter of a triangle is $$18$$ feet and its sides are consecutive integers, what is the middle side's length?

Accepted Answer

$$6 ft$$

Question 15

If Jim earned $$x$$ dollars, Bill earned $$3x$$ dollars, and Tom earned $$x+5$$ dollars, what is the total amount earned?

Accepted Answer

$$4x + 5$$

Question 16

A child sells $$x$$ cups at $$\2$ and y$ cups at $$\$$3$$, with $$x + y = 50$$ and $$2x + 3y = 124. $$What is the value of $$x$$?

Accepted Answer

$$26$$

College Algebra Study Notes: Word Problems and Linear Equations

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