System of Equations

Question

The cost of 3 apples and 7 tangerines is $2.10. Four apples and 3 tangerines cost $1.85. Set up the system of equations to find the cost of each apple and tangerine.

Group of answer choices

A.3A + 7T = 2.10

B.4A + 3T = 1.85

C.3(A + T) = 2.10

D.4(A + T) = 1.85

E.3A + 7T = 2.10

F.4A - 3T = 1.85

G.3A + 7T + 2.10

H.4A + 3T + 185

Answer 1

I'm a bit confused. Your question states you want the "system of equations" (plural) but each answer only has one equation. Unless you can pick multiple? Either way here is the solution:

3 Apples + 7 Tang = $2.10 (1)

4 Apples + 3 Tang = $1.85 (2)

This could be options (A) and (B) on your sheet. However, if we're turning the system of equations into one equation then:

Rearrange equation (1):

3 Apples = $2.10 - 7 Tang

Divide by 3 to get unit apple amount:

1 Apples = ($2.10 - 7 Tang)/3 (3)

Plug equation (3) into (2):

4 * (($2.10 - 7 Tang)/3) + 3 Tang = $1.85

$2.80 - 6.333 Tang = $1.85

Evaluate:

$0.95 = 6.333 Tang

Divide by 6.333 to find price of unit Tang:

Tang = $0.15 (4) - Also the price for 1 tangerine

Now use equation (4) to find the price of apples by putting back into equation (1):

3 Apples + 7 ($.15) = $2.10 (4) into (1)

3 Apples = $2.10 - 7($.0.15)

3 Apples = $1.05

Apples = $0.35