GED Mathematical Reasoning
Writing Equations from Words
This is translation, not calculation. The whole skill is turning English into symbols. Once the equation is written, solving it is the easy part — and the test gives plenty of points just for setting it up correctly.
The words first
- per / each
- means multiply by how many
- is / was / totals
- means equals
- more than / increased by
- means add
- less than
- means subtract — but watch the order
- twice / triple
- means multiply by 2 / by 3
The method
THE WORD-TO-SYMBOL TABLE
is, was, gives, totals → =
more than, increased by, sum → +
less than, fewer, decreased → −
of, per, each, times, twice → ×
per, split, shared, divided → ÷
THE "LESS THAN" TRAP — it reverses the order
5 less than x → x − 5 (NOT 5 − x)
x less than 5 → 5 − x
THE STANDARD SHAPE OF A TEST WORD PROBLEM
total = starting amount + (rate × how many)
$40 to start, $15 each week, total $145:
145 = 40 + 15w
ALWAYS SAY WHAT THE LETTER MEANS
"let w = number of weeks" — one line, prevents most errors.
Worked all the way through
The problem
A plumber charges a $60 call-out fee plus $45 an hour. Write an equation for the total cost C after h hours, then find the cost of a 3-hour job.
- Step 1 — Identify the part that never changes.The $60 call-out is charged once, no matter how long. That is the starting amount.
- Step 2 — Identify the part that depends on time.$45 for every hour. That is a rate, so it multiplies the hours: 45h.
- Step 3 — Put them together.C = 60 + 45h
- Step 4 — Now use it. Put 3 in for h.C = 60 + 45(3)
- Step 5 — Multiplication before addition.45 × 3 = 135, then 60 + 135 = 195
On the board
C = 60 + 45h
flat fee + rate × hours
C = 60 + 45(3)
put 3 in for h
C = 60 + 135
multiply before adding
C = 195
h = 0 → C = 60 ✓
check: no hours still costs the call-out
Answer
C = 60 + 45h, and a 3-hour job costs $195
A second one, in a different form
"Seven less than twice a number is 19." Find the number.
twice a number → 2n
seven less than that → 2n − 7
less than REVERSES the order
2n − 7 = 19
"is" means equals
2n = 26
add 7 to both sides
n = 13
divide both sides by 2
Answer
13
The usual mistake
Reversing subtraction and division phrases.
Check yourself
Test your equation with an easy number before trusting it. Zero hours should cost $60 — put h = 0 in and you get C = 60 ✓. If a zero-hour job came out at $0, the call-out fee was left out.
Practice it
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