# Difference between revisions of "Euclid 2018"

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b) Given <math>\frac{a}{6}</math> + <math>\frac{6}{18}</math> = 1, find the value of a | b) Given <math>\frac{a}{6}</math> + <math>\frac{6}{18}</math> = 1, find the value of a | ||

− | c) The total cost of one chocolate bar and two identical packs of gums is | + | c) The total cost of one chocolate bar and two identical packs of gums is 4.15 dollars. One chocolate bar costs 1 dollar more than one pack of gum. Find the price of a chocolate bar. |

+ | |||

+ | == Solution == | ||

+ | a) Plug x = 11 back to the original equation | ||

+ | |||

+ | (11) + (11+1) + (11+2) + (11+3) = <math>\boxed{50}</math> | ||

+ | |||

+ | b)By simplifcation: | ||

+ | |||

+ | <math>\frac{3a}{18}</math> + <math>\frac{6}{18}</math> = 1 | ||

+ | |||

+ | <math>\frac{3a+6}{18}</math> = 1 | ||

+ | |||

+ | <math>3a + 6 = 18</math> | ||

+ | |||

+ | <math>3a = 12</math> | ||

+ | |||

+ | <math>a = 4</math> | ||

+ | |||

+ | Therefore a = <math>\boxed{4}</math> | ||

+ | |||

+ | c) Set One chocolate bar as x + 1 and one piece of gum as x dollars. We get: | ||

+ | <math>2(x) + (x + 1) = 4.15</math> | ||

+ | <math>3x + 1 = 4.15</math> | ||

+ | <math>x = 1.05</math> | ||

+ | |||

+ | Therefore one piece of chocolate bar is 1 + 1.05 = <math>\boxed{2.05}</math> | ||

+ | |||

+ | ~ North America Math Contest Go Go Go | ||

== Video Solution == | == Video Solution == |

## Latest revision as of 15:44, 11 April 2021

## Problem

a) Given x = 11, find (x) + (x+1) + (x+2) + (x+3)

b) Given + = 1, find the value of a

c) The total cost of one chocolate bar and two identical packs of gums is 4.15 dollars. One chocolate bar costs 1 dollar more than one pack of gum. Find the price of a chocolate bar.

## Solution

a) Plug x = 11 back to the original equation

(11) + (11+1) + (11+2) + (11+3) =

b)By simplifcation:

+ = 1

= 1

Therefore a =

c) Set One chocolate bar as x + 1 and one piece of gum as x dollars. We get:

Therefore one piece of chocolate bar is 1 + 1.05 =

~ North America Math Contest Go Go Go