Expressions Using Letter-numbers: questions with answers

Kabir is older, so Kabir's age is Ravi's age with 5 added to it, which is $r + 5$. Subtracting would give the age of someone 5 years YOUNGER than Ravi.

$d$ says how many candles are bought and $s$ says how many kilograms of sugar are bought. Both can be replaced by different numbers on different days. Buying one more candles adds Rs 12 to the amount. Only the two prices, Rs 12 and Rs 45, stay fixed.

Equal expressions must give the same value for ANY value of the letter. Here they agree only at $y = 5$. At $y = 6$, $3y$ gives 18 while $y + 10$ gives 16. So the two expressions are equal at some values and different at others.

Adding $a$ twice and $d$ twice gives $2a + 2d$. Opening the bracket in $2(a + d)$ also gives $2a + 2d$. The two expressions simplify to the same thing, so they give the same perimeter for every pair of side lengths.

11 plates of Pongal at Rs 45 bring in 495, and 13 plates of Vada at Rs 12 bring in 156. Together that is 651. Each price must stay with the count of its own dish; swapping them gives 717.

The 15 seconds of starting up happen ONCE, however much there is to grind, so that number is added on its own. Only the 9 seconds are charged for each kg of grain, so they are multiplied by $y$, giving $15 + 9y$.

Written in terms of the middle date, the four arms are $c - 7$, $c - 1$, $c + 1$ and $c + 7$. Adding all five, the $-7$ cancels the $+7$ and the $-1$ cancels the $+1$, leaving five lots of $c$: the sum is $5c$ wherever the shape is placed. That is why the answer can be written at all without knowing which dates were chosen.

Moving one place to the RIGHT adds 1, but moving one row DOWN skips a whole week of seven cells, so the date below $d$ is $d + 7$. $d + 1$ is the date to the right of $d$, not the one below it.

Put the whole value into the bracket, minus sign and all: $-6 + 1 = -5$. Multiplying by 3 gives -15. Leaving the minus sign behind would make the bracket 6 + 1 = 7 and the answer 21, a positive number where the true value is negative.

The letter carries its minus sign into both places it appears. $-h$ becomes $-(-2)$, which ADDS 2, while $4h$ becomes 4 x $(-2)$, which SUBTRACTS 8. So the value is 11 + 2 - 8 = 5. Treating the subtraction as an ordinary one gives 1; ignoring the minus sign altogether gives 17.

$9h$ and $h$ are like terms, and the lone $h$ counts as one of them, so they leave 8 of them. The 7 carries no letter and cannot join them, so the simplest form is $8h + 7$.

The minus sign subtracts the WHOLE bracket, so every sign inside is reversed as it comes out: $7 - 2 + 6v$, which is $5 + 6v$. The $6v$ was being taken away inside the bracket, and taking away a subtraction adds it back.

Step 1 uses 3 matchsticks, and every step after it adds 2 more, so Step $n$ uses $3 + 2(n - 1)$, which simplifies to $2n + 1$. $3n$ is right at Step 1 but wrong ever after, because the pattern grows by 2 each time and not by 3. $2n$ grows correctly but is one short throughout, since Step 1 needs 3 and not 2.

The first pentagon costs 5, and each of the other $(m - 1)$ costs 4, so the total is $5 + 4(m - 1)$, which simplifies to $4m + 1$. Notice the multiplier is the STEP-UP 4, not the first count 5: multiplying by 5 is right only at $m = 1$.

$6y - 4$ is a sum of the terms $6y$ and $-4$. The first is 6 x 5 = 30, and taking 4 away leaves 26. Reading it as 6 x (5 - 4) would give 6, which is what $6(y - 4)$ means.