Aboy bought 3 cakes and 4 pies from a shop and received $7.50 change from $40. if he had bought 4 cakes and 3 pies from the same shop, then he would have received $0.75 change instead. how much did he pay for each cake and each pie?

the cost of a cake is $8.5

the cost of a pie is $1.75

Step-by-step explanation:

Let x = the cost of a cake

Let y = the cost of a pie

A boy bought 3 cakes and 4 pies from a shop and received $7.50 change from $40. This means that the cost of the 3 cakes and 4 pies is 40-7.5 = $32.5. Therefore,

3x + 4y = 32.5 - - - - - - - -1

If he had bought 4 cakes and 3 pies from the same shop, then he would have received $0.75. This means that the cost of the 4 cakes and 3 pies is 40-0.75 = $39.25. Therefore,

4x + 3y = 39.25 - - - - - - - -2

Multiply equation 1 by 4 and equation 2 by 3. It becomes

12x + 16y = 130

12x + 9y = 117.75

Subtracting ,

7y = 12.25

y = 12.25/7 = 1.75

From equation 1,

3x = 32.5 - 4y

3x = 32.5 - 4×1.75 = 32.5 - 7

3x = 25.5

x = 25.5/3 = $8.5

- "runner b is moving at a slower rate."

- "the graphs shown are graphs of distance(km) against time(min).

the slopes of this graphs are are given by:

slope = (change in y)/(change in x)

= (change in distance)/(change in time)

this is the formula for finding the speed. so, the slope of these graphs represent the speed of the runner.

taking each division in the graph to represent 1 on both axis:

runner a ⇒ speed = (2-0)/(1-0)

= 2/1

= 2 km/min

runner b ⇒ speed = (3-0)/(3-0)

= 3/3

= 1 km/min

this shows that   runner b is moving at a slower rate."

c. 1,233 miles