![okokalyssa](/avatars/39695.jpg)
okokalyssa
31.07.2019 •
Mathematics
Marianne has been collecting donations for her biscuit stall at the school summer fayre. there are some luxury gift tins of biscuits to be sold at £5 each, normal packets at £1 each, and mini- packs of 2 biscuits at 10p each. she tells amy that she has received exactly 100 donations in total, with a collective value of £100, and that her stock of £1 packets is very low compared with the other items. amy wants to work out how many of each item marianne has. show how she can do it.
Solved
Show answers
More tips
- F Food and Cooking 10 Reasons Why You Should Avoid Giving Re-Gifts: An Informative Guide...
- S Sport How to wrap boxing hand wraps? Everything you need to know!...
- A Animals and plants 5 Tips for Taking Care of Yews to Keep Them Green and Beautiful...
- H Health and Medicine How to Calm Your Nerves? Expert Tips That Actually Work...
- O Other What is a Disk Emulsifier and How Does it Work?...
- S Sport How to Pump Your Chest Muscle? Secrets of Training...
- C Computers and Internet How to Get Rid of 3pic Infector: Everything You Need to Know...
- S Style and Beauty How to Grow Hair Faster: Real Methods and Advice...
- C Computers and Internet How to Top Up Your Skype Account Without Losing Money?...
- C Computers and Internet How to Get Rid of Spam in ICQ?...
Answers on questions: Mathematics
- M Mathematics 8. A school raffle sold 480 tickets. Students were charged $1/ticket and teachers $5/ticket. The total receipts were $560. How many of each ticket were sold? 9. An airplane...
- M Mathematics What was the rate of economic growth for Sudan?...
- W World Languages E, help pls cefbvfhjvek...
- C Chemistry If you evaporated 125 mL of a 3.5 M solution of iron(II) nitrite, how many moles of iron(II) nitrite would you recover?...
- M Mathematics If a score in a distribution changes in numerical value, it will necessary change...
- M Mathematics Describe what would be true about the rate of change in a situation that could be represented by a graphed line and an equation in the form y=mx + b...
Ответ:
Number of normal packets sold at £1 each: 2
Number of mini- packs of 2 biscuits sold at 10p each: 80
Solution:
Number of luxury gift tins of biscuits sold at £5 each: x
Amount received by the number of luxury gift tins of biscuits sold: £5 x Number of normal packets sold at £1 each: y
Amount received by the number of normal packets sold: £1 y
Number of mini- packs of 2 biscuits sold at 10p each: z
Amount received by the number of 2 biscuists sold: 10p z =£0.1z
She tells Amy that she has received exactly 100 donations in total:
(1) x+y+z=100
A collective value of £100:
Total amount receibed: £5 x + £1 y+ £0.1z= £100 → £ (5x+1y+0.1z)= £100 → 5x+y+0.1z=100 (2)
Her stock of £1 packets is very low compared with the other items:
y<<x
y<<z
Then we can despice the value of "y" and solve for "x" and "z":
y=0:
(1) x+y+z=100→x+0+z=100→x+z=100 (3)
(2) 5x+y+0.1z=100→5x+0+0.1z=100→5x+0.1z=100 (4)
Solving the system of equations (3) and (4) using the substitution method:
Isolating z in equation (3): Subtrating x from both sides of the equation:
(3) x+z-z=100-x→z=100-x
Replacing z by 100-x in the equation (4):
(4) 5x+0.1z=100→5x+0.1(100-x)=100
Eliminating the parentheses:
5x+0.1(100)-0.1x=100→5x+10-0.1x=100
Adding similar terms on the left side of the equation:
4.9x+10=100
Solving for x: Subtrating 10 from both sides of the equation:
4.9x+10-10=100-10→4.9x=90
Dividing both sides of the equation by 4.9:
4.9x/4.9=90/4.9→x=18.36734693
Replacing x=18.36734693 in the equation:
z=100-x→z=100-18.36734693→z=81.63265306
We can round x and z: x=18 and z=81 and solve for y in equations (1) and (2):
(1) x+y+z=100→18+y+81=100
Adding similar terms on the left side of the equation:
99+y=100
Subtracting 99 from both sides of the equation:
99+y-99=100-99→y=1
(2) 5x+y+0.1z=100→5(18)+y+0.1(81)=100→90+y+8.1=100→98.1+y=100→98.1+y-98.1=100-98.1→y=1.9→y=2 different to 1
Suppose y=1. Replacing y=2 in equations (1) and (2):
(1) x+y+z=100→x+1+z=100→x+1+z-1=100-1→x+z=99
(2) 5x+y+0.1z=100→5x+1+0.1z=100→5x+1+0.1z-1=100-1→5x+0.1z=99
Repeating the process:
z=99-x
5x+0.1z=99→5x+0.1(99-x)=99→5x+9.9-0.1x=99→4.9x+9.9=99→4.9x+9.9-9.9=99-9.9→4.9x=89.1→4.9x/4.9=89.1/4.9→x=18.18367346
z=99-18.18367346→z=80.81632653
x=18 and z=80
(1) x+y+z=100→18+y+80=100→y+98=100→y+98-98=100-98→y=2
(2) 5x+y+0.1z=100→5(18)+y+0.1(80)=100→90+y+8=100→y+98=100→y+98-98=100-98→y=2
Number of luxury gift tins of biscuits sold at £5 each: 18
Number of normal packets sold at £1 each: 2
Number of mini- packs of 2 biscuits sold at 10p each: 80
Ответ:
I think it’s A.
Step-by-step explanation: