Question

Kyra went to the grocery store on Monday and bought 5 apples and 2 oranges for a total of $3.45. On Thursday she bought 3 oranges and 7 apples for a total of $4.90. What is the cost of apples and oranges?

Answer 1

apples cost $0.55 each, orange costs $0.35 each

Explanation:

let apples be a, let the oranges be o

make equations:

• 5a + 2o = $3.45 ............equation 1

• 3o + 7a = $4.90 ............equation 2

make a the subject for equation 1:

`\sf 5a + 2o = $3.45`

`\sf 5a = 3.45 - 2o`

`\sf a = (3.45 - 2o)/(5)`

solve:

`3o + 7(\sf (3.45 - 2o)/(5)) = $4.90`

`\sf 0.2o+4.83=4.9`

`\sf o=0.35`

each orange cost $0.35

For apples:

`\sf a = (3.45 - 2o)/(5)`

`\sf a = (3.45 - 2(0.35))/(5)`

`a=0.55`

each apples cost $0.55

Answer 2

Apple = $0.55

Orange = $0.35

Explanation:

Let A = cost of an apple

Let R = cost of an orange

Monday: 5A + 2R = 3.45

Thursday: 3R + 7A = 4.90

Rewrite 5A + 2R = 3.45 to make R the subject:

⇒ 2R = 3.45 - 5A

⇒ R = 1.725 - 2.5A

Substitute R = 1.725 - 2.5A into 3R + 7A = 4.90 and solve for A:

⇒ 3(1.725 - 2.5A) + 7A = 4.90

⇒ 5.175 - 0.5A = 4.90

⇒ 0.5A = 0.275

⇒ A = 0.55

Substitute found value for A into 5A + 2R = 3.45 and solve for R:

⇒ 5(0.55) + 2R = 3.45

⇒ 2.75 + 2R = 3.45

⇒ 2R = 0.7

⇒ R = 0.35