Question

HELP. Elaine bought a total of 15 shirts & pants. She bought 7 more shirts than pants. How many of each did she buy?

Answer 1

You need to use the equation of:
\[x+x+7=15\]

To solve for this, let's add up the x's. Since there are two x's, we know that it is 2x. Our next equation will be:
\[2x+7=15\]

Now subtract 7 from both sides. 15-7=8. Making the next equation to:
\[2x=8\]

To find x we have to divide:
\[8\div2=4\]

x=4

Answer 2

An example of one problem was

Chapter 3 Equations in Two Variables

Lesson 3−8 Solve Systems of Equations Algebraically
Page 247

Solve the system y = x – 10 and y = –12 algebraically.
Since y = x − 10 and y = −12, substitute −12 in for y in the first equation and solve for x.

y = x − 10 Write the equation.
−12 = x − 10 Replace y with −12.
−12 + 10 = x − 10 + 10 Addition Property of Equality
−2 = x Simplify.

Since y = −12, the solution to the system is the point (−2, −12).


The cost of 8 muffins and 2 quarts of milk is $18. The cost of 3 muffins
and 1 quart of milk is $7.50. How much does 1 muffin and 1 quart of
milk cost? Write and solve a system of equations. Use a bar diagram if needed. Interpret the solution.

Let x = the cost for 1 muffin and y = the cost for 1 quart of milk.
8x + 2y = 18 8 muffins and 2 quarts of milk cost $18.
3x + y = 7.5 3 muffins and 1 quart of milk cost $7.50.

Solve for y in the second equation.
3x + y = 7.5 Write the equation.
3x − 3x + y = 7.5 − 3x Subtraction Property of Equality
y = 7.5 − 3x Simplify.

Since 8x + 2y = 18 and y = 7.5  3x, substitute 7.5  3x in for y in the first equation and solve for x.
8x + 2y = 18 Write the equation.
8x + 2(7.5  3x) = 18 Replace y with 7.5  3x.`
8x + 15  6x = 18 Distributive Property
2x + 15 = 18 Simplify.
2x = 3 Addition Property of Equality
x = 1.5 Division Property of Equality

Since x = 1.5, substitute 1.5 for x in the equation y = 7.5  3x.
y = 7.5  3x Write the equation.
y = 7.5 – 3(1.5) Replace x with 1.5.
y = 3 Simplify.

The solution is (1.5, 3). This means that one muffin costs $1.50 and one quart of milk costs $3.