Solving the equation is the mechanical part, the one you already know how to do. The hard part, and the one that really matters, is setting it up: turning a problem written in words into an equation (or a system). With a clear method and a few templates, most problems become routine.
Consecutive numbers: if the first is $x$, the next is $x+1$, and the one after is $x+2$.
Ages: use a table with "today" and "in"/"ago" a certain number of years. Time passes equally for everyone, so you add (or subtract) the same amount to each age.
Today
In 8 years' time
Younger brother
$x$
$x + 8$
Older brother
$2x$
$2x + 8$
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Find three consecutive integers such that the sum of the first two is $15$ units greater than the third number.
Find three consecutive integers such that the sum of the first two is $15$ units greater than the third number.
On a social network, Alba has three times as many followers as her brother Javier. If Alba were to lose $150$ followers and Javier were to gain $50$, both would have…
On a social network, Alba has three times as many followers as her brother Javier. If Alba were to lose $150$ followers and Javier were to gain $50$, both would have exactly the same amount. How many followers does each currently have?
In geometry, always draw the figure and write the measurements using $x$. Then use the perimeter formula (the sum of all the sides).
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In a video game shop, they have sold twice as many handheld consoles as desktop consoles. If they have sold a total of $18$ consoles, how many have they sold of each…
In a video game shop, they have sold twice as many handheld consoles as desktop consoles. If they have sold a total of $18$ consoles, how many have they sold of each type?
A farmer wants to fence off a triangular plot for his sheep. Knowing that it is an isosceles triangle, that the unequal side measures $5$ metres less than each of the…
A farmer wants to fence off a triangular plot for his sheep. Knowing that it is an isosceles triangle, that the unequal side measures $5$ metres less than each of the equal sides and that a total of $40$ metres of fencing was needed, how long is each side of the plot?
When a problem has two independent quantities and two conditions, set up a system with $x$ and $y$ instead of struggling to fit it into a single letter.
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In a café, they have mixed Colombian coffee, which costs $12$ €/kg, with Brazilian coffee, which costs $8$ €/kg. If they obtained $20$ kg of mixture and its final price…
In a café, they have mixed Colombian coffee, which costs $12$ €/kg, with Brazilian coffee, which costs $8$ €/kg. If they obtained $20$ kg of mixture and its final price is $9$ €/kg, how many kilograms of coffee of each type did they use?
A water tank is filled by two taps. Tap A takes $6$ hours longer than tap B to fill the tank on its own. If both are opened at the same time, the tank fills in exactly…
A water tank is filled by two taps. Tap A takes $6$ hours longer than tap B to fill the tank on its own. If both are opened at the same time, the tank fills in exactly $4$ hours. Calculate how long tap B would take to fill the tank on its own. (This problem requires solving a quadratic equation).