Creating Algebraic Expressions Often the number we are looking for is not defined as “a number”, but rather as a real-life unknown value. For example. We have a bag of cherries and we know there are c cherries in the bag. Mr. Chida eats 10 of the cherries, leaving 4 cherries remaining. Write an equation representing this situation. It is important to note the units the variable is defined in. c is defined as an unknown number of cherries. there are c cherries in this bag – = c – 10 = 4

Write mathematical statements representing the following situations: 1.We have a bag of cherries and we know there are d cherries in the bag. Mr. Chida eats 3 of the cherries, leaving 7 cherries remaining. 2. We have another bag of cherries and we know there are e cherries in the bag. Mr. Chida picks 20 new cherries from his garden and adds them to the sack. There are now 40 cherries in this sack.

Creating Algebraic Expressions Example 2. let there be p marbles in a box. Mr. Chida has emptied 3 boxes of marbles on his table and there are 36 marbles there Write an equation representing this situation. 3 x p = 36 there are p marbles in this box = 3p = 36

Write mathematical statements representing the following situations: 1.There are four boxes of marbles containing s marbles each. Altogether the boxes contain 32 marbles. 2. From those four boxes, 8 marbles are removed. Now there are 24 marbles altogether. 3. Five bigger boxes are bought in containing f marbles each. We don’t like the cat’s eyes marbles so we remove them from the collection. Altogether 10 are removed. In the end we are left with 40 marbles. Solve the equation to find out how many there were originally were in the bigger boxes of marbles.

Creating Algebraic Expressions Example 2. let a tree be h metres tall when Mr. Chida bought it After a while it has grown 2 metres to a total height of 8m. Write an equation representing this situation. take note of the units h is defined in (metres) h + 2 = 8 tree is h metres tall = + 2 metres taller 8 metres

Write mathematical statements representing the following situations: 1.Let the height of a palm tree Mr. Chida buys be d metres. How tall would the tree be if you cut the top two metres off? 2. If the new height is 4m (after chopping the top 2m off) what was the initial height of the tree?

Example 4. let the temperature today be t o C The temperature tomorrow is going to be 3 times as hot. Tomorrow’s temperature is 33 o C Write an equation representing this situation. take note of the units t is defined in ( o C) 3 x t = 33 todays temp is t o C todays temp (t o C) 33 o C = 3t = 33 TOMORROW’S TEMPERATURE

Write mathematical statements representing the following situations: 1.Let the Good Friday temperature be x o C. By the next day the temperature has halved. The temperature the next day is 11 o C. Find out what the Good Friday temperature was.

Example 5. Jeans are on Sale at CHEENZ UNLTD. They cost $35 each. Loretta wants to buy as many as she can with $175. Using x as the number of jeans write an expression for the situation and find out how many jeans Loretta can buy. One jean will cost $35 Two jeans will cost $70 Three jeans will cost $105 this can be thought of as 1 x 35 this... 2 x 35 and this... 3 x 35 x jeans will cost x x 35 35x so cost of jeans = 35x but question also tells us cost of jeans = 175 so x = 175

1.YoYos at Chids R Us cost $4 each. Write an expression for the cost of y YoYos 2. Wiremu wants spend $44 on the YoYos. Add this to your earlier expression to form an equation. 3. How many YoYos can Wiremu buy? 4. Digital pet devices are $7 per toy. How much will Ariana pay for d digital pets? 5. Ariana spends $28 on the digital pets. How many does she buy? 7.Nelly spends $2 per ring at the toy store. She buys r rings. She spends $24 on them. Write an equation for this situation and solve to find the number of rings purchased by Nelly. 6. Tomhasntsung phones are selling their new T6 phones for $900 each. Jimmy’s family buy p phones. Write an expression for the price Jimmy’s family paid for the phones

Example 5(II). Jeans are still on sale at CHEENZ UNLTD. Damien wants to buy 5 of exactly the same pair of jeans. The jeans cost z dollars each. When Damien goes to the shop he spends $125 altogether. Write an eqation for the situation. One jean will cost $z Two jeans will cost $z + $z Three jeans will cost $z + $z + $z this can be thought of as 1 x z this... 2 x z and this... 3 x z 5 jeans will cost 5 x z 5z so cost of jeans = 5z but question also tells us cost of jeans = 125 so.... 5z = 125

1. Damien’s sister arwa buys 3 tops at the same store costing t dollars each. Write an expression for this situation. 2. Arwa spends $66. Write an equation 3. Solve to find out how much Arwa spent. 4. Damien buys 2 bracelets at the store which cost $b each. He spends 7.50 on these. Write an equation and solve to find out how much Damien spent on bracelets.

MODELLING PAYMENTS. Equations are Commonly Used to model payment schemes. Just remember, hourly charges are rates, so they need to be multiplied by the number of hours to find the TOTAL HOURLY CHARGE The fixed charge does not vary, so we don’t need to attach any variable to it, just add it on the end. Eg. A painter charges $40 as a fixed charge and $ 35 per hour depending on the size of job. The painter works for h hours. If the painter charges $110 for the job, how many hours did she work? Hourly total: =35 x h =35h Fixed charge: =40 (no matter what) Total charge = 35h + 40 Total charge was 110 so 35h+40 = 110

1.Sam’s plumbing business charges $32 an hour and $10 fixed charge. One day Sam works for h hours and makes $106. Write an equation for the above and solve to find out how many hours Sam worked. 2. Theodore’s party planners charge $25 for coming to do the job and $30 for every hour they work. They came to plan Wendy’s party. It took m hours and costed Wendy $130. Write an Equation and work out how long it took to plan Wendy’s party? 3. Timon’s Taxi company charges a $4 flag fall and $1.50 per km. Natalie travels with them for k km. She spends $7. How far did she travel? 2. Leslie delivers newspapers every Sunday. Every Sunday she is guaranteed $10 plus $0.02 per newspaper. On Monday she delivers n newspapers and makes $12. How many newspapers did she deliver?