An SAT Math micro-topic under Linear equation word problems (Algebra). Free to read — no account needed.
The key to a word problem is to assign a letter to each unknown, then translate the sentence piece by piece into symbols. Once every phrase is turned into math, the equation writes itself.
Learn the common translations: "10more thanx" is x+10; "8less thanx" is x−8; "twice x" is 2x; "52 of x" is 52x; and "the product of x and y" is xy.
A comparison becomes an equation with the two sides set equal. "If Jake loses 8 pounds he will weigh twice as much as Sarah" becomes j−8=2s: the changed quantity on one side, what it equals on the other.
When a problem gives two facts about two unknowns, write one equation for each to form a system. "A customer buys 5 items for $120, with shirts at $20 and pants at $30" becomes s+p=5 and 20s+30p=120.
Worked examples
Write an equation: John gets 52 of Kyle's pocket money x. "of" means multiply, so John gets 52x.
Write an equation: if Emma gains 12 pounds she will weigh 1.5 times as much as Sarah, where their weights are e and s. The changed weight equals 1.5 times Sarah's: e+12=1.5s.
A shop sells 45 baskets of apples and peaches for $324; apples cost $6 and peaches cost $9. Write a system for the numbers a and p. Count of baskets: a+p=45. Money: 6a+9p=324.
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