Writing Expressions and Formulae

Start with n and decide which operation “more than” describes.

Add six equal lengths, or multiply one length by six.

Start with m and take away nine.

Equal sharing uses division.

“From 14” tells you the starting value.

Follow the two operations in their stated order.

1. Multiplying a by 3 gives 3a.
2. Adding 2 then gives 3a+2.

Make the sum first; twice applies to that whole sum.

1. The sum of t and 5 is t+5.
2. Double all of it: 2(t+5). This is also 2t+10.

Put brackets around the whole result that is divided.

1. The first result is b-4.
2. Dividing the whole result by 3 gives \frac{b-4}{3}.

Perimeter adds the four equal sides.

1. The perimeter is w+w+w+w.
2. Four copies of w give 4w cm.

Separate the charge for every ticket from the charge paid once.

1. The tickets cost 9s pounds.
2. Add the one booking charge: C=9s+6.

Find Lily’s age before doubling it.

1. Lily is younger than Omar, so her age is x-4.
2. Her brother’s age is twice this: 2(x-4), or 2x-8.

Find the total spent, then subtract it from the amount paid.

1. Three notebooks cost 3p pounds.
2. Change is money paid minus money spent: 20-3p.

Find each type of ticket cost separately, then add.

1. Four adult tickets cost 4a pounds. Seven child tickets cost 7c pounds.
2. The total is 4a+7c. The two letters represent different prices, so do not combine them into 11ac.

Add two lengths and two widths, keeping the extra numbers.

1. Add the four sides: (2x+3)+(x+2)+(2x+3)+(x+2).
2. The letter terms total 6x and the numbers total 10. The perimeter is (6x+10) cm.

Both amounts are spent. Also check whether the option is an expression or a formula.

1. Subtract both amounts spent from 30: 30-x-y.
2. x+y-30 subtracts the wrong way round: it takes the £30 away from what he spent.
3. The bracketed option 30-(x-y)=30-x+y adds the cost of the pen instead of subtracting it.

Which amounts are paid once, and which amount is paid for every hour?

Part (a)

1. The hours cost 3h pounds. The fixed fee (£5) and the helmet (£2) are each paid once.
2. C=3h+5+2, which simplifies to C=3h+7.

Part (b)

1. Substitute h=6: C=3\times6+7=18+7=25.
2. The hire costs £25.

Find how many seats the two rows remove before accounting for the separate seats.

1. The original rows contain 5n seats. Removing two rows removes 2\times5=10 seats.
2. The three separate seats stay, so S=5n-10+3=5n-7. Equivalently, 5(n-2)+3 counts the rows remaining first.

Apply the discount to the cards before adding delivery.

1. Before the discount, the cards cost 7p. Half off means the customer pays half, \frac{7p}{2}.
2. Delivery is added after the discount, so C=\frac{7p}{2}+4. The £4 delivery is not halved.

Add all four sides, then include the separate amount for the bow.

1. The perimeter is (x+3)+x+(x+3)+x=4x+6.
2. Add 8 cm for the bow: 4x+6+8=4x+14.

Form money received minus both costs; only one of the costs depends on n.

Part (a)

1. Ticket money is 8n. Refreshments cost 2n and the hall costs 35 once.
2. P=8n-2n-35=6n-35.

Part (b)

1. Use n=25: P=6\times25-35.
2. 150-35=115, so £115 is left.