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57 problems match “linear equations”. Clear

Boys and total strength of a class ●○○○○ 10 ptsIn a class, $\frac{2}{3}$ of the students are boys and the rest, 17 students, are girls. (i) How many boys are in the class? (ii) What is the total number of students in the class?
Blue balls with twice the red probability ●○○○○ 10 ptsA bag contains 6 red balls and some blue balls. The probability of drawing a blue ball from the bag is twice the probability of drawing a red ball. Find the number of blue balls in the bag.
Coefficients of an algebraic identity ●○○○○ 10 ptsThe equation $ax+18=2(x-b)$ holds for all values of $x$ . Work out the value of $a-b$ .
Missing angles of a heptagon ●○○○○ 10 ptsFive angles of a heptagon have measures $80^\circ$ , $85^\circ$ , $175^\circ$ , $90^\circ$ and $140^\circ$ . The other two angles are congruent. Find the measure of each of the other two angles, in degrees.
Greatest integer in a set of five ●○○○○ 10 ptsFive positive integers have an average of 15. What is the greatest possible value of one of these integers?
Harmonic numbers ●○○○○ 10 ptsCall three numbers $a, b, c$ harmonic when their reciprocals form an arithmetic sequence, that is, $\frac{1}{a}-\frac{1}{b}=\frac{1}{b}-\frac{1}{c}$ . For example, $15, 12, 10$ are harmonic because $\frac{1}{12}-\frac{1}{15}=\frac{1}{10}-\frac{1}{12}$ . Given that $x$ , $5$ , $3$ are harmonic numbers in this order with $x>5$ , find $x$ .
Height of a cuboid from its edges ●○○○○ 10 ptsA cuboid has a base measuring 8 cm by 10 cm. The total length of all its edges is 92 cm. Find the height of the cuboid in centimetres.
Maximum burning time of a candle ●○○○○ 10 ptsA candle with an original length of $12\ \text{cm}$ burns so that its remaining length depends on the burning time as shown in the table below: | Burning time (minutes) | $10$ | $20$ | $30$ | $40$ | $50$ | $\ldots$ | |---|---|---|---|---|---|---| | Remaining length (cm) | $11.2$ | $10.4$ | $9.6$ | $8.8$ | $8$ | $\ldots$ | Assuming the remaining length decreases linearly with burning time, find the maximum number of minutes the candle can burn.
Finding a parameter from a known root ●○○○○ 10 ptsIf the solution of the equation $\frac{3}{10}a+\frac{2x+4}{2}=4(x-1)$ is $x=3$ , find the value of $a$ .
Unknown parameter from a root ●○○○○ 10 ptsIf $x=3$ is a root of the equation $\frac{a-2}{x}-\frac{1}{x-2}=0$ , find the value of $a$ .