Earnings and Deductions

Worked example

1. 1

   $44.5-38=6.5$ — Find the overtime hours first: everything after the first 38 hours. That is 6.5 hours.

2. 2

   $38\times 16=608$ — The normal pay: 38 hours at the normal $16 rate.

3. 3

   $16\times 1.25=20$ — The overtime rate. 25% more means 100% + 25% = 125% of $16, so multiply by 1.25.

4. 4

   $6.5\times 20=130$ — The overtime pay: overtime hours × overtime rate.

5. 5

   $608+130=\$738$ — Add the normal pay and the overtime pay to get the week’s total pay.

Worked example

1. 1

   $38\times 15=570$ — Normal pay first: 38 hours at the normal $15 rate.

2. 2

   $1.5\times 15=22.50$ — The overtime rate. Time and a half means 1.5 × the normal rate.

3. 3

   $795-570=225$ — Take the normal pay off the week’s pay. What is left was earned in overtime.

4. 4

   $225÷22.50=10$ — Each overtime hour pays $22.50, so divide to count the hours: 10 hours.

Worked example

1. 1

   $6\times 11=66$ — The basic pay: 6 hours at $11 an hour.

2. 2

   $90-66=24$ — Take the basic pay off the total. What is left, $24, is the bonus.

3. 3

   $24÷4=6$ — The bonus is 4% of the sales. Divide by 4 to find 1% of the sales: $6.

4. 4

   $6\times 100=\$600$ — 100% of the sales is 100 times 1%. So she sold $600 of goods.

5. 5

   $0.04\times 600=24$ — Check: 4% of $600 is $24, and 66 + 24 = 90. It matches the pay in the question.

Worked example

1. 1

   $3\times 2.45=7.35$ — The notebooks: number bought × price of one, so 3 lots of $2.45.

2. 2

   $2\times 1.80=3.60$ — The pens, the same way: 2 lots of $1.80.

3. 3

   $7.35+3.60=10.95$ — Add the two amounts. This is the total cost of the shopping.

4. 4

   $20-10.95=\$9.05$ — Change is the note minus the total. It is less than $20, so it makes sense.

Worked example

1. 1

   $20-4.25=15.75$ — Find what he spent. The note minus the change is the total cost.

2. 2

   $3\times 2.65=7.95$ — The sandwiches: number bought × price of one.

3. 3

   $7.95+1.40=9.35$ — Add the juice. Now you have everything you know.

4. 4

   $15.75-9.35=6.40$ — Take the known costs off the total. What is left is the price of the 4 cakes together.

5. 5

   $6.40÷4=\$1.60$ — The 4 cakes cost the same, so divide by 4 to get the price of one.

Worked example

1. 1

   $10-2.50=7.50$ — Pay for the notebook first. The money left is what you can spend on pencils.

2. 2

   $7.50÷0.85=8.82\dots$ — Divide the money left by the price of one pencil to see how many fit.

3. 3

   $8\text{ pencils}$ — Round DOWN. You cannot buy part of a pencil, and 9 would cost more than you have.

4. 4

   $8\times 0.85=6.80$ — If they ask for the change, first find what the 8 pencils cost.

5. 5

   $7.50-6.80=\$0.70$ — The change: money left minus the cost of the pencils.

Worked example

1. 1

   $20=6\times 3+2$ — Split the 20 cans into offer groups of 3 (2 paid, 1 free): 6 full groups and 2 cans left over.

2. 2

   $6\times 2=12$ — In each full group you pay for only 2 cans, so 12 paid cans.

3. 3

   $12+2=14$ — The 2 left-over cans are not in a full group, so you pay for them too.

4. 4

   $14\times 0.90=\$12.60$ — Number of cans you pay for × the price of one can.

Worked example

1. 1

   $3.40÷2=1.70$ — The small bag: price ÷ kilograms gives the price of 1 kg, $1.70.

2. 2

   $8.25÷5=1.65$ — The big bag, the same way: $1.65 for 1 kg.

3. 3

   $1.65<1.70$ — The 5 kg bag is better value, because each kilogram costs less. Say which bag AND give both prices.