A group of related facts that use the same number is a fact family
When ever you have percentages, it should be helpful to bear in mind you can express them as multipliers. In this case, it will be helpful.
So, if we let:
a = test score
b = target score
then, using the information given:
a = 1.1b + 1
a = 1.15b - 3
and we get simultaneous equations.
'1.1' and '1.15' are the multipliers that I got using the percentages. Multiplying a value by 1.1 is the equivalent of increasing the value by 10%. If you multiplied it by 0.1 (which is the same as dividing by 10), you would get just 10% of the value.
Back to the simultaneous equations, we can just solve them now:
There are a number of ways to do this but I will use my preferred method:
Rearrange to express in terms of b:
a = 1.1b + 1
then b = (a - 1)/1.1
a = 1.15b - 3
then b = (a + 3)/1.15
Since they are both equal to b, they are of the same value so we can set them equal to each other and solve for a:
(a - 1)/1.1 = (a + 3)/1.15
1.15 * (a - 1) = 1.1 * (a + 3)
1.15a - 1.15 = 1.1a + 3.3
0.05a = 4.45
a = 89
Answer:
x = √39
General Formulas and Concepts:
<u>Pre-Algebra</u>
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
<u>Trigonometry</u>
- [Right Triangles Only] Pythagorean Theorem: a² + b² = c²
Step-by-step explanation:
<u>Step 1: Identify</u>
Leg <em>a</em> = <em>x</em>
Leg <em>b</em> = 5
Hypotenuse <em>c</em> = 8
<u>Step 2: Solve for </u><em><u>x</u></em>
- Substitute [PT]: x² + 5² = 8²
- Isolate <em>x</em> term: x² = 8² - 5²
- Exponents: x² = 64 - 25
- Subtract: x² = 39
- Isolate <em>x</em>: x = √39
Answer:
864
Step-by-step explanation:
(4)(108)(2)
=(432)(2)
=864
You would pay $1100.15 (rounded to nearest hundredths)(unrounded would be 1100.14875)
