15. Substituting values into equations (Practice Equations)

Bob works in a bakery and makes $24$ cheese straws per hour.

If Bob works $7$ hours a day and $5$ days a week, how many cheese straws does he make in a week?

Answer: $840$

Wrong Answers:

$600$

$800$

$864$

WORKING:

$24\times7=168$ cheese straws a day

$168\times5=840$ cheese straws a week.

Carol is hiring a plumber to fix her boiler. The plumber charges $£20$ an hour plus a fixed fee of $£15$ .

If it takes $4$ hours to fix the boiler, how much will Carol have to pay?

Answer: $£95$

Wrong Answers:

$£180$

$£80$

$£115$

WORKING:

Hourly rate of $£20$ per hour $\times4=£80$

£80+£15=£95

$y=x^2+7x-8$

If $x=3$ , what is the value of $y$ ?

Answer: $22$

$19$

$8$

$-20$

WORKING:

y=3^2+(7\times3) - 8 = 22

What is the value of $\dfrac{5ab}{c^2}$ to $2$ decimal places?

Answer: $0.83$

Wrong Answers:

$5$

$0.42$

$2.5$

WORKING:

$\dfrac{5\times2\times3}{6^2}=\dfrac{30}{36}=0.8\dot{3}=0.83$ to $2$ decimal places.

Daniel works for a supermarket. He earns $£8$ an hour Monday to Saturday and $£10.50$ an hour on Sundays.

If Daniel works for $8$ hours on Saturday and $6$ hours on Sunday, how much will he earn over the weekend?

Answer: $£127$

Wrong Answers:

$£112$

$£147$

$£124$

WORKING:

(£8\times8) + (£10.50\times6)=£127

The number of sandwiches needed for a birthday party is calculated using the formula:

$S=3a+2c$ ,

where $a$ and $c$ are the amount of adults and children respectively who attend the party.

If $20$ adults and $30$ children go, how many sandwiches will be needed?

Answer: $120$

Wrong Answers:

$100$

$130$

$110$

WORKING:

S=(3\times20) + (2\times30) = 120

The surface area of a hemisphere is calculated using the formula:

$S_h=3\pi r^2$

If $r=6$ and using the value of $3.14$ for $\pi$ , calculate the surface area of the hemisphere to $1$ decimal place.

Answer: $339.1$

Wrong Answers:

$339.3$

$56.52$

$169.56$

WORKING:

3\times3.14\times6^2=339.1

Kevin is parking his car in a car park in the city centre. It costs $£2.50$ per hour between the hours of 08:00 and 18:00. And then a one off fee of $£2$ for the period 18:00 to 08:00.

Kevin parks his car from 10:00 till 20:00 and has a $20%$ .

How much will it cost him?

Answer: $£17.60$

Wrong Answers:

$£13.60$

$£22$

$£4.40$

WORKING:

10:00 – 20:00 = $8$ hours.

$8$ hours $\times£2.50=£20$

$£20+£2=£22$

$20%\text{ of } £22 = £4.40$

$£22-£4.40=£17.60$

$a=4b^2-12c+\dfrac{d}{3}$

If $b=7$ , $c=8$ , $d=9$ , what is the value of $a$ .

Answer: $103$

Wrong Answers:

$-65$

$109$

$295$

WORKING:

a=4\times7^2-12\times8+\dfrac{9}{3}=196-96+3=103

Q10

$S=\dfrac{\sqrt{T}}{U^2-V^2}$

If $T=25$ , $U=3$ and $V=6$ , what is the value of $S$ to $3$ decimal places?

Answer: $-0.185$

Wrong Answers:

$0.185$

$-1.667$

$-0.926$

WORKING:

S = \dfrac{\sqrt{25}}{3^2-6^2}=-0.185